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Basic Electricity & Electronics
2
SEMICONDUCTOR
A semiconductor is a substance which has specific resistively ( 10-4 to 0.5 Ω m ) in between
conductor and insulators. Examples – Germanium, Silicon, carbon etc.
Crystal structure of Germanium or Silicon :
A substance in which atoms or molecules arranged in an orderly pattern is known as a Crystal .
Germanium / Silicon are tetravalent compounds. An atom of Ge (or Si) has four valence electron. It
shares four valence electron from Ge (or Si) atoms lying around it. In this way it completes octave of
electrons in its outer most shell to assume a stable
electronic structure stability. All atoms take part in the
way to have the stable crystal structure.
The sharing of the electrons shown covalent
bonds which binds atoms close together. These
bonds are strong enough and no free electron is
available at absolute zone. With the increase of the
temperature covalent bonds go on breaking which
have electrons to conduct. So semiconductors
(intrinsic) at higher temperature conduct to some
extent.
Types of Semiconductors :
Semiconductor
Intrinsic semiconductors are extremely pure form.
An extremely pure semiconductor is known as intrinsic type semiconductor. It conducts with
the increase of temperature. When some impurities are mixed (rather doped) to semiconductors for the
purpose of conduction, it is called extrinsic semiconductor. Impurities are of two types (i) pentavalent
substances like Arsenic (As) & Antimony (Sb) and (ii) trivalent substances ( like Gallium and
Indium )
Extrinsic Semiconductor
Intrinsic
Semiconductor
P - Type N - Type
Fig 1: Ge / Si Crystal
3
n – Type Semiconductor:
Pentavalent substance like Arsenic or Antimony when doped into the Ge (or Si) crystal it
constitute a n–type semiconductor. That is when a
small amount pentavalent impurities is added to a
pure semiconductor, it is called a n-type
semiconductor.
The figure shows that the four electrons
valence of As atom form covalent bond with
surrounding Ge atoms, but the rest one electron is
left free in the crystal. These free electrons take part in conduction. As the charge of the carrier
(here electron) is negative the semiconductor type is called n-type.
p – Type Semiconductor:
Trivalent substance like gallium, indium when doped into Ge (or Si) crystal it constitute a p-type
semiconductor. That is when a small amount of trivalent impurities is added to a pure
semiconductor, is called a p-type semiconductor.
The figure shows that the three electrons
(valence) of Ge atom form three complete covalent
bonds with the surrounding Ge atoms, but a
covalent bond is incomplete for the want of an
electron. This absent electron is called a hole. In p-
type semiconductor such holes are present which, when P.D. is applied to it fillup the holes
creating hole at their own place. In this way holes move and take part in conduction in p-type
semiconductor. Holes are equivalent to a positive charged particles. The conductor is known as
p-type semiconductor.
Lack of electron in covalent bond contributes a hole
Extra unbounded electron of As atom
Fig: n type crystal
Fig: p- type Crystal
4
The p – n Junction
P – type semiconductor is suitably joined to n – type semiconductor, the contact surface is called
a p – n junction.
When the junction is so formed then some electron from n –
type (where its concentration is more) gets diffused to the p – type
semiconductor. Some holes are recombined with these electrons at the
junction which create a negatively charged layer at this junction in p–
type area. As some electrons have crossed the junction, appositive charged layer at the junction in the n
–type area is also created. These two layers together form a potential barrier at the junction, called
Depletion layer.
Forward Bias p – n junction : When the external voltage applied to the junction is in
such a direction that it eliminates the potential barrier, thus
allowing current flow, it is called forward Biasing
In such a connection, battery supplies electron and
repels them to p – n junction in the n- type region. This reduces
and finally eliminates the potential barrier. On the other hand the
positive terminals of the battery attract electrons which are
coming out of the p-type region. In the p-type region, holes
movement occurs from +ve electrode to the junction.
So in forward biasing the p – n junction allows the current through it. Holes carry current in p–
type region and electron in n – type region.
Reverse Bias p – n junction
When the external voltage applied to the junction is
in such a direction that potential barrier is increased, it is
called reverse biasing.
In such a connection, electrons in n-type region
move towards the =ve plate of the battery and the holes in p-
type region move towards the –ve plate of the battery cause
wide of potential barrier. Hence a p-n junction does not allow
current.
Conclusion: The p-n junction allows current in one direction. For this, a p-n junction is called
Semiconductor Diode Valve of Rectifier.
Depletion layer +
+
+
+
-
-
-
-
p n
Fig I : p-n junction
O
O
O
O
p n
Fig II : Forward bias p-n junction
O O
O
O
p n
Fig III : Reverse bias p-n junction
5
Characteristics of p-n junction:
Fig-1 shows the circuit arrangement for drawing a forward
bias characteristic. It will be used with reversed polarity of
battery for reverse bias characteristic.
Forward Bias Characteristic:
The first quadrant shows (in fig 2), the forward bias
characteristic. It is seen that at first (region OA) the current
increases very slowly and the curve is non linear. It is
because the external applied voltage is used up in overcoming the potential barrier. However once the
external voltage exceed the potential barrier voltage, the p-n junction behaves like an ordinary conductor.
Therefore current rises very sharply with increases in external voltage (region AB on the curve). The
curve almost linear.
Reverse Bias Characteristic:
In the reverse bias to the p-n junction potential barrier at the
p-n junction increases. Therefore the junction resistance becomes
very high and practically no current flows through the circuit.
However in practice a very small current (of the order µA ) flows in
the circuit with reverse bias as shown in the reverse characteristics.
This is called reverse saturation current (Is) and it is due to the
minority carriers.
If the reverse voltages increased continuously kinetic energy
of the electrons (minority carriers) may become high enough to
knockout electrons from the semiconductor atoms. At this stage
break down of the junction occurs, characterized by a sudden rise of reverse current and a sudden fall of
the resistance of the barrier region. This may destroy the junction permanently.
Breakdown Voltage: It is the minimum reverse voltage at which p-n junction breaks down with sudden
rise in reverse current.
Knee Voltage: It is the forward voltage at which the current through the junction starts to increase
rapidly.
0.1 0.2 0.3 0.4 15 10 5
200
150
100
50
0
100
200
300
400
0
IR (µA)
IF (mA)
VF (volt) VR(volt)
Breakdown Potential
Knee voltage
( Fig -2 )
A
B
( Fig -1 )
6
RECTIFICATION
The electric power available is 220 V, AC 50 Hz. It can be used directly for lighting heating etc,
but there are many applications (e.g. electronic circuits) where D.C. supply is needed. Conversion of AC
into DC is made through rectifier and the process is called rectification.
Half Wave Rectification:
Fig 1 shows a circuit diagram of the half wave rectifier.
The main supply is connected to a transformer. The output of
transformer is connected in series with a diode and the load.
Operation :
Fig 2(a), shows the wave nature of AC supply. The
transformer output also has the same nature (only change
found in the amplitude). This has positive and negative both voltage values. In one half cycle diode falls
under forward bias and current conduction takes place through load RL. In the next half cycle the diode
falls under reverse bias and the current conduction remains off.
In this way only positive half cycle remains
present in the output. The output is shown in fig
2(b). this is called half wave rectification.
Disadvantage:
1. The pulsating current supplied to the load
under which all circuit will not work.
2. This requires elaborate filtration which is
not easy.
3. output is found low as half of the cycles
are used.
Full wave rectifier:
The circuit employs two diodes D1 and D2 as shown
in the fig 1. A centre tapped transformer with
secondary winding wires connected with two diodes.
The primary winding is connected to the main supply.
RL is load resistance, T is a centre tapped
transformer with taps at A, O and B. RL is the load
which is connected to the output of the circuit.
Operation: In the half cycle of the main supply (at the
output of transformer) A is positive with respect to O and B is negative with respect of O. This time D1 is
in forward bias condition and it allows current through it which flows through the load but D2 is in reverse
bias condition which does not allow current through it.
t
t
Input
voltage
Half wave Rectified
Output
( a )
( b )
volRL
Fig. 1
Fig. 1
RL Output
T
A
B
D1
D2
7
In the next half cycle A becomes negative with
respect to O and B becomes positive with respect to
O. this time D2 is in forward bias which allows current
through it, which also flows though the load, but D1 is
in reverse bias condition which does not allow current
though it.
That is, in both the half cycles current flows
through the load in the same direction. The voltage
appearing across the load is shown in fig 2B. This is
called full wave rectification, where all half cycles
are present.
Disadvantage of a centre tapped rectifier:
1. It is difficult to locate the centre tap on the secondary winding.
2. the DC out put is small as each diode utilizes only one half of the transformer secondary
voltage.
3. The diode used must have high peak inverse voltage.
Bridge Rectifier: This is a full wave rectifier. It requires four diodes, it does not require centre tapped
transformer. The circuit connection is shown in the fig 3.
Operation: In a half cycle
of mains supply when A
remains positive with
respect to B, D1 and D3,
conduct to flow current
through the load RL, when
D2 and D4 do not conduct.
In this way full wave
rectification happens.
Advantages:
1. The need for centre tapped transformer eliminated.
2. The output is twice that of the centre tapped circuit for the same secondary voltage
3. the peak inverse voltage is one half that of the centre tapped circuit ( for same DC output)
t
t
Input
voltage
Full wave Rectified Output
( a )
( b )
Fig. 2
RL
D1 D2
T
Fig.3
Output
A
B
D3 D4
8
Disadvantages:
1. It requires four diodes
2. In each half cycle two diodes, in series, conduct which drops potential double as compared
to centre tapped rectifier.
FILTER CIRCUITS
I. Capacitor Filter:
In the above figure a capacitor filter circuit is shown, output of
the full wave rectified is fed to the input of the circuit and
output of it is shown
in fig c.
Charging of capacitor
takes place with the
increase of voltage
and charging happens up to peak value VM. After being
reached to VM, the voltage falls sharply. At this time the
capacitor is discharged through which may be slower than the
falling of voltage. The output appears more smooth. As the falling of voltage occurs due to discharge of
capacitor through load, the output filtration due to discharge of capacitor through load, the output filtration
depends on the load.
II. Choke Input Filter:
Choke input filter is
shown above. The
input is the output
of a full wave
rectifier ( as shown
in fig a). The
inductor L always
opposes variation
of current
producing back
e.m.f.. Sharp
variation in voltage is is smoothen by the inductor L. It allows Dcs intact but ACs with some change. The
AC port passing through it is mostly bypassed through the capacitor as it creates a low reactance path for
ACs. Finally the output obtained is smoother to some extant as shown in fig c.
(b) Input wave to filter circuit t
V
t
V
(c) Output wave of capacitor
filter circuit
RL Rectifier Input
(a) Choke Input Filter:
RLRectifier Input
(a) Capacitor filter
(b) Input wave to filter circuit t
V
t
V
(c) Output wave of Choke input
filter
Vm
9
III. Capacitor Input Filter or π- Filter:
Fig a shows the voltage output of a full wave rectifier which is fed to the input of the filter circuit.
1) The first capacitor ( C1: input capacitor) offers
a low reactance by pass path to the AC and
allows DC to pass over to the inductor L.
2) The inductor L smoothes the rest part of AC
voltage and by clipping the sharp bends of the voltage curve.
3) The rest AC part getting a further by pass as given by the capacitor C2. Hence the output is
found nicely filtered as shown in figure c
ZENER DIODE
Zener diode is a properly doped crystal diode which has sharp break down voltage.
Zener diode is like an ordinary diode that is properly doped so as to have sharp break
down voltage. It is always used with reverse bias condition.
It has forward bias characteristic as similar to that of an
ordinary diode. Its reverse bias characteristic has a knee (
break down voltage) at VZ (as shown). Where the break
down occurs. The break down causes an avalanche which
generates high value of current. Zener diode does not burn
at break down voltage like ordinary p-n junction diode.
The symbol of a Zener diode is shown in fig 1a.
The avalanche and break down helps a Zener diode to it as
voltage regulator.
Voltage Regulation with a Zener Diode: A voltage
regulation circuit with a Zener diode is shown in fig 2. The
Zener diode is connected in reverse bias across the load RL, across which the constant output is desired.
The series resistance R is chosen in such a way that the potential drop across the Zener diode becomes
equal to the break down voltage VZ, i.e.
Operation: When the input voltage increases, reverse bias voltage across the Zener diode exceeds the
value VZ. The Zener diode will go to the break down condition and current through it (IZ) will increase and
simultaneously current (I) through the series resistance R will increase which will create a voltage drop
across R, keeping the output voltage Vo. In this way higher input voltage is regulated.
(b) Input wave to filter circuit t
V
t
V
(c) Output wave of π - Filter
200
150
100
50
0
100
200
300
400
0
0.1 0.2 0.3 0.4 15 10 5
IR (µA)
IF (mA)
VF (volt) VR(volt)
Breakdown Potential
Knee voltage
Vo = VZ = VI – I R
RL I / P
C1 C2
(a) π- Filter Circuit
Fig: 1 (a)
Vm
10
Now if the input voltage Vi falls below VZ, the Zener diode does not conduct ( as the break down does not
occur) and out put voltage accordingly falls. For this reason the input voltage is kept at high value
compared to VZ.
TRANSISTOR
Transistor is a semiconductor which consists two p-n junction caused by sandwiching one type of
semiconductor between a pair of other type.
Transistors are of two types (i) n-p-n and (ii) p-n-p
In each type of transistor, the following points may be noted.
1. There are two p-n junctions therefore a
transistor may be regarded as a combination of
two diodes connected back to back.
2. There are three terminals taken from each type
of semiconductor.
3. The middle section is a very thin layer. This is
the most important factor in the function of a
transistor.
Emitters, base and collectors:
The transistor has three regions namely emitters, base and collectors. The base is much thinner
than the emitter, while collector is wider than both as shown in the above figure.
Emitter is heavily doped so that it can inject a large number of charge carriers (electrons or
holes) into the base. The base is lightly doped and very thin; it passes most of the emitter injected charge
carriers to the collector. The collector is moderately doped.
The emitter - base junction ( forward biased) is very small compared to collector – base junction
(reverse biased).
Working of n-p-n transistor:
The figure shows the n-p-n transistor with forward bias to emitter-base junction and reverse bias
to collector-base junction. The forward bias causes the
electrons in the n-type emitter to flow towards the base.
This constitutes the emitter current IE. As these electrons
flow though the p-type base, they tend to combine with
holes. As the base is lightly doped and very thin, therefore,
only a few electrons (less than 5%) combine with the holes
to constitute the base current IB. The remainder (more than
95%) cross over into the collector region to constitute collector current IC. In this way, almost the entire
emitter current flows in the collector circuit. It is clear that IE = IB + IC
n
nn p
n
n np
IE
IB
IC
11
Working of p-n-p transistor:
The figure shows the basic connection of a p-n-p transistor> The forward bias causes the holes in the p-
type emitter to flow towards the base. This constitutes the emitter current IE. As these holes cross into n-
type base, they tend to combine with the electrons. As the
base is lightly doped and very thin, therefore only a few
holes (less than 5%) combine with the electrons. The
remainder (more than 95%) cross into the collector region to
constitute collector current IC. In this way almost the entire
emitter current flows in the collector circuit.
Here also
IE = IB + IC
p p n O
O O
O
O
OO
O
O
O O
O
p – n – p Circuit n – p – n Circuit
12
AMPLIFIERS
1. Single stage amplifier 2. Multi-stage Amplifier
Single Stage Amplifier
When a weak signal (Alternating) is fed to the base of transistor, a small base current (alternating) starts
flowing. Due to the transistor action a much larger ( β times
the base current0 alternating current flows through the
collector load Rc. As the value of Rc is quite high (usually 4 –
10 KΩ), therefore a large voltage variation appears across
Rc. thus a weak signal applied in the base circuit appears is
amplified form in the collector circuit. It is in this way a
transistor acts as amplifier.
Practical circuit of a Single Stage Amplifier
Phase reversal occurs in CE Amplifiers. This is
shown in the figure. In common base (CB) and
common collector (CC) amplifier, no phase
reversal occur.
1. The resistances R1, R2, and RE form
the biasing and stabilization circuit. This
biasing must establish a proper
operating point, otherwise a part of the
–ve half cycle of the signal may be cut-
off in the output.
2. Input capacitor Cin (≈ 10µF allows only A.C. signal and isolates the signal source from R2. If it is
not used then the source resistance of signal may change the bias.
3. emitter bypass capacitor CE ( ≈ 100 µF ) provides a law reactance path to the amplified A.C.
signal will pass through RE causing voltage drop across it, thereby reducing the output voltage.
4. Coupling capacitor CC ( ≈ 10µF ) couples one stage of amplification to the next stage. If it is not
used bias condition of the next stage will not be drastically changed due to RC. Also it allows to
pass the AC part of signal to the next stage.
Vcc
Output R1
R2 RE
RC5 KΩ
RC5 KΩ
Vcc
VOut
R1
R2 RE
VOut
t
13
Multi-Stage Amplifier Transistor Amplifier
A transistor containing more than one stage amplifiers, is known as multistage transistor
amplifier.
Few Terms
1. Gain : The ratio of the output electrical quantity to the input of one of the amplifier is
called its gain.
The gain of a multistage amplifier is equal to the product of gain of individual stages
G = G1 x G2 x G3 ……
2. Frequency Response : The voltage
gain of an amplifier varies with signal frequency.
It is because of reactance of the capacitor in the
circuit changes with signal frequency and hence
affect the voltage gain and signal frequency is
known as frequency response.
3. Decibel Gain : .
Out
in
PPowerGain
P=
10( ). log Out
in
PBel PowerGain
P=
1 bel = 10 decibel ( or 10 db ) .
10log10
POutPowerGainPin
∴ = db .
Power input = Vin Iin = Iin2R .
Power Output = VOut IOut = IOut2 ROut .
Band Width : The range of frequency over
which the gain is equal to or greater than
70.7% of the maximum gain is known as
bandwidth. .
.
Frequency
fr
Max.
Amplifier Vin VOut
fr f1
Max. Gain
Frequency
f2
0.707 gain
Band Width
f1 = Lower cut-off frequency,
f2 = Upper cut-off frequency,
Fall in voltage ( from maximum gain) gain
= 20 log10100 – 20 log10
= 20 log ( 100 / 70.7 ) db.
= 3 db. .
14
R-C Coupled Transistor Amplifier :
A two stage R-C coupled transistor amplifiers shown below. A coupling capacitor Cc is used to
connect the output of the 1st stage to the input of the 2
nd stage. As the coupling from one stage to the
next is achieved by a coupling
capacitor followed a high resistor,
therefore such amplifier are called
Resistance-Capacitance coupled
Amplifiers.
The resistance R1,R2, & RE
form biasing and stabilizing network.
The emitter bypass capacitor CB
offers low reactance path to the
signal. Without it voltage gain os each
stage would be lost. The coupling
capacitor CC transmits A.C. signal but
blocks D.C. This prevents D.C. interference between various stages and shifting of operating potential.
Operation : When A.C. signal is applied to the base of the transistor, it appears in amplified form
across its collector resistance Rc. The amplified signal developed across Rc is given to the base of the
next stage through coupling capacitor Cc. The 2nd stage does further amplification of the signal. In this
way the cascaded (one after another ) stages amplify the signal and overall gain is considerably
increased.
It is important to note that the gain in the 1st stage falls to some extent due to the shunting effect
of the input resistance of second stag. Thus the total gain is found less than the product of gains of
different stages.
Frequency Response: The figure shows the frequency response of a typical R-C coupled amplifier.
Between 50 Hz to 20 KHz the frequency response curve is flat i.e.
gain is uniform. So this is excellent for an audio amplifier.
At low frequency (< 50 Hz) reactance of coupling capacitor is
very high, hence a vary from one stage to the next stage. Moreover,
CE can not shunt emitter resistance RE effectively because of its large
resistance at low frequencies.
At high frequency (> 20 KHz), the reactance of Cc is very
small and it behaves as short circuit. This increases the loading effect
of the next stage and serves to reduce voltage gain. Moreover at high frequency capacitive reactance of
base – emitter junction is low which increases the base current. This reduces the current amplification
factor β. Due to these two reasons the voltage gain drops off.
ADVANTAGES:
1. It has excellent frequency response. The gain is constant over the audio frequency range.
2. It has lower cost since resistor and capacitor are cheap in market.
3. The circuit takes small space.
VOut
Vcc
RC R1
R2 RE
RC R1
R2 RE
1st stage 2
nd stage
50 Hz 200 KHz Frequency
15
DISADVANTAGES:
1. The R – C coupled amplifier have low voltage and power gain. [ It is because of low resistance
presented by the input of each stage to the preceding stage decreases the effective load
resistance (R&C) and hence the gain.
2. They have the tendency to become noisy with age, particularly in moist climate.
3. Impedance matching is poor. The output impedance is several hundred ohm where as the input
of the speaker is only a few ohms. Hence little power will be transferred to the speaker.
APPLICATION:
The R – C coupled amplifier have excellent audio fidelity over a wide range of frequency.
Therefore it is widely used as voltage amplifiers (preamplifier) in the audio system. For poor
impedance matching it is not used in final stage (i.e. Power amplifier)
Transformer Coupled Amplifier
[The main reason for low voltage and power gain of R-C Coupled amplifier is that the effective
load (RAC) of each stage is decreased due to the low resistance presented by the input of each stage to
the preceding stage. If the effective load resistance of each stage could be increased, the voltage and
power gain could be increased. This can be achieved by transformer coupled amplifier. By the use of
impedance changing properties of transformer the low resistance of a stage (load) can be reflected as a
high load resistance to the previous stage.]
figure shows two stages of transformer coupled amplifier. A coupling transformer is used to feed
the output of one stage to the input of the next stage. The primary P of this transformer is made the
collector load and the secondary S gives the input to the next stage.
Operation : When an A.C. signal is applied to the base of first transistor, it appears in the amplified
form across primary P of the coupling transformer. The voltage
developed across primary is transferred to the input of the next
stage by the transformer secondary. The second stage renders
amplification in an exactly similar manner.
Frequency Response : The frequency response in transformer
coupled amplifier is poor. Flat response is found for a very low
band width. This is why it is not suitable in …….. At low
S
R1
R2 RER2 RE
1st stage 2
nd stage
CECE
P VOut
Vcc
R1 P
S
Coupling Transformer Output Transformer
Frequency
16
frequencies, the reactance of primary begins to fall resulting decrease in gain. At high frequencies, the
capacitance between turns of winding acts as a bypass capacitor to reduce the output voltage and hence
the gain. It follow, therefore that there will be disproportionate amplification of frequencies in a complete
signal such as music, speech etc. This introduces frequency distortion.
It may be added that with a properly designed transformer, it is possible to achieve a fairly
constant gain over the audio frequency range.
ADVANTAGES:
1. No signal power is lost in the collector or base resistors.
2. Excellent impedance matching can be achieved in transformer coupled amplifier.
3. Due to excellent impedance matching, transformer coupled amplifier provides higher gain.
DISADVANTAGES:
1. It has a poor frequency response.
2. The coupling transformers are bulky and fairly expensive.
3. Frequency distortion is higher. Amplificaiton is higher for higher frequency signals.
4. This has tendency to hum at the output.
APPLICATIONS:
Transformer coupled amplifier is mostly used in impedance matching. In general the last stage of
multistage amplifier is the power stage. For maximum power transfer, the impedance of power source
should be equal to that of load. This is achieved by designing a transformer with proper turn ratio.
Direct Coupled Amplifier :
In low frequency application (e.g. amplifying photoelectric current, thermo couple current etc.)
this type of the amplifier is used. In this one stage is directly connected to the next stage without any
intervening coupling device. This type of the coupling is known as direct coupling.
Circuit Operation : The signal (weak) is applied to the input of first transistor T1. Due to transistor
action, an amplified output is obtained across the collector load Rc of transistor T1. This voltage drives the
base of the second transistor and amplified out put in obtained across its collector load. In this way direct
coupled amplifier raises the strength of weak signal.
ADVANTAGES
1. .This circuit arrangement is simple because of minimum use of resistors.
2. The circuit has low cost.
Output
17
DISADVANTAGES
1. It can not be used for amplifying highfrequencies.
2. The operating point is shifted due to temperature variation.
Comparison of different types of coupling
S.N Particulars R – C Coupling Transformer Coupling Direct Coupling
1 Frequency response Excellent is audio frequency range
Poor Very Poor
2 Cost Less More Least
3 Space and Weight Less More Least
4 Impedance matching Not good Excellent Good
Oscillator
An electronic device that generates sinusoidal oscillation of desired frequency is known as a
sinusoidal oscillator.
Tank Circuit: A circuit which produces electrical oscillations of any desired frequency is known as an
oscillatory circuit or tank circuit.
Operation: fig-1(a) shows a tank circuit. Suppose the capacitor is charged from a D.C. source with
polarity as shown in figure un-bracketed.
1. When the switch ‘S’ is closed, the capacitor ‘C’ will discharge through inductance ‘L’ and current
‘I’ flows in the direction as shown. Due to inductive effect of ‘L’ the current builds slowly towards
the maximum value. The current will be maximum when the capacitor fully discharged. At this
moment the electrostatic energy of the capacitor is zero, but because of electron motion is
greatest (i.e. maximum current), the magnetic field energy around the coil is maximum. That is,
the entire electrostatic energy of capacitor is completely converted into magnetic field energy
around the coil.
2. Once the capacitor is discharged, the magnetic field begins to collapse and produces a counter
e.m.f.. According to Lenz’s law the counter e.m.f. will keep the current flowing in the same
direction . This will charge the capacitor with opposite polarity as shown under bracket.
Fig: 1 (a) Tank circuit
L C (+)
+ ( ) t
Fig: 1 (b) Wave form of oscillation in Tank circuit
I
18
3. After the collapse of the field, the capacitor begins to discharge. Now current flows in the
opposite direction. The frequency for charging and discharging results in alternative motion of
electrons are an oscillating current. The energy is alternately stored in the electric field of the
capacitor ‘C’ and the magnetic field of the inductance coil ‘L’. This interchange of energy
between L &C is repeated over and again resulting the production of resistive and radiation
losses in the coil and dielectric loss in the capacitor. During each cycle, a small part of the
originally imparted is used up to overcome the losses. This result to tha6t the amplitude of the
oscillating current decreases gradually and eventually it becomes zero. That is a tqank circuit
produces a damped oscillation as shown in the Fig 1(b).
Frequency of the oscillation 1
2f
LCπ=
Un-damped Oscillation from Tank Circuit
To overcome the energy lose, we have to supply the lost amount of energy in every cycle. This
can be done with a positive feedback amplifier.
Steps of an Oscillator
1) The tanks circuit oscillates with
frequency 1
2f
LCπ= with
Amplitude of oscillation diminishes with time.
2) The oscillation is fed to a transmitter amplifier which amplifies the amplitude of oscillation but the
out put phase gets inverted.
3) A part of the output of the amplifier is fed further to the feed back network whuch invents the
phase of signal further and adds to the tank circuit.
Amplifier
Feed Back
Network
Input
(Vin)
Output
(Vout) Vf
Fig 2 (a)
Transistor Amplifier
Feed Back
Circuit
L C
Fig 2 (b)
19
Hartley’s Oscillator
The figure shows a Hartley’s oscillator. It uses a centre tapped inductor with parts L1 and L2 and a
capacitor C. The tank circuit is made up of L1, L2, & C whose frequency of oscillation is given by
Where LT = L1 + L2 + M
M Ξ Mutual inductance between L1 & L2
Circuit Operation :
When the circuit is turned on, the capacitor is charged. When this capacitor is fully charged, it
discharges through coils L1 & L2, setting up oscillations of frequency determined by expression (1). The
output voltage of the amplifier appears across L1 and feedback
voltage across L2. The voltage across L2 is 180o ahead of phase
with the voltage developed across L1 (Voutput) as shown in figure. It
is easy to see that voltage feed back (i.e. across L2) to the
transistor provides positive feedback. A phase shift of 180-o- is
produced by the transistor and further phase shift of 180O is
produced by L1 – L2 voltage divider. In this way, feed back is properly phased to produce continuous un-
damped oscillations.
Feed back fraction :
VOutput
R1
R2 RE
L1 C
L2
180o + 180
o
RF Choke
Vcc
180o
C
1
2 T
fL Cπ
=
2 2
1 1
f
f
out
V I L Lm
V I L L
ω
ω= = =
VOut L1 L2 Vf
C
20
Colpitt’s Oscillator :
The figure shows a Colpitt’s
Oscillator. It uses two capacitors
placed across a common inductor L
and the centre of the two capacitor is
taped. The tank circuit is made up of
C1, C2 & L. the oscillator frequency is
Where 1 2
1 2
T
C CC
C C=
+
Circuit Operation :
When the circuit is turned on, the capacitors C1 and C2 are charged. The capacitors discharge
through L, setting up oscillations of frequency determined by expression (1). The output voltage of the
amplifier appears across C1 and feedback voltage is developed across C2. The voltage across C2 is 1800
out of phase with the voltage developed across C1 (Voutput). It is easy to see that voltage feedback
(voltage across C2 ) to the transistor provides a positive feedback of phase shift of 180o is produced by
C1 – C2 voltage divider. In this way, feed back is properly phased to produce continuous un-damped
oscillation.
Feedback fraction f
Out
Vm
Vν =
2
1
IC
IC
ω
ω
=
1
2
Cm
Cν⇒ =
R2 RE
C
VOutput
R1
C1 L
C2
180o + 180
o
RF Choke
Vcc
180o
VOut Vf
L
C1 C2
+ -
+ - - +
1
2 T
fLCπ
= (i)
21
MODULATION AND DEMODULATION
In radio transmission it is necessary to send audio signal (e.g. music, speech etc.) from a
broadcasting station over a great distance to a receiver. This communication of audio signal is made
without any wire. The audio signal can not be sent too far without employing enormous amount of
energy. The energy of the wave is directly proportional to frequency. At audio frequency (20 Hz to 2
KHz), the signal power is quite small and the radiation is not practicable. Energy is practicable only at
high frequencies e.g. above 20 KHz. The high frequency signal can be sent thousand of miles even with
comparatively low power.
For the above reason the audio signal is super imposed on high frequency carrier wave. The
process of super imposition of a audio signal (or corresponding a electrical signal) onto a carrier wave
(radio wave) is called a modulation.
At the radio receiver, the audio signal is extracted from the modulated wave by the process
called De-modulation.
The signal is then amplified and reproduce into sound by the loud speaker.
Modulation :
The process of changing some characteristic (e.g. amplitude, frequency or phase) of a carrier
wave in accordance with the intensity of the signal is known as modulation.
Modulations are basically of three types:
1. Amplitude modulation
2. Frequency modulation
3. Phase modulation
Modulator Oscillator
AudioAmplifier
Receiver
Fig-1: Block diagram of Transmission system of radio waves.
22
Amplitude Modulation
When the amplitude of high frequency carrier wave is changed in accordance with the intensity of
the signal, it is called Amplitude modulation.
The amplitude modulation is done with the following suppositions:
(i) The amplitude of the carrier wave changes according to the intensity of the signal.
(ii) The amplitude variation of the carrier wave is at the signal frequency fs
(iii) The frequency of amplitude modulated wave remains the same i.e. carrier frequency fc.
Modulation factor: The ratio of the change of amplitude of carrier wave to the amplitude of normal
carrier wave is called Modulation Factor (m)
Analysis of Amplitude Modulated Wave :
A carrier may be represented by
ec = Ec Cos ωc t
In amplitude modulation, the amplitude of carrier wave is varied in accordance eith the intensity of the
signal. Suppose the modulation factor is m. It means that the signal produces a maximum change m Ec
in carrier amplitude. Therefore, the signal can be represented by
es = m Ec Cos ωs t
Therefore the amplitude of A.M. wave is
Amplitude change of carrier wave
Amplitude of Normal carrier wave Modulation Factor (m) =
Where ec Ξ Instantaneous voltage of carrier Ec Ξ Amplitude of carrier ωc = 2 πfc Ξ angular frequency
Where es Ξ Instantaneous voltage of carrier m Ec Ξ Amplitude of carrier
ωs = 2 πfs Ξ angular frequency of signal
EC A.M. Wave
m EC
Signal
m EC
Carrier Wave EC
Fig. I : Modulation Factor
23
= Ec + m Ec Cos ωs t = Ec(1 + m Cos ωs t )
The instantaneous voltage of AM wave is
ec = Ec(1 + m Cos ωs t ) x Cos ωc t
= Ec Cos ωc t + m Ec Cos ωs t . Cos ωc t
= Ec Cos ωc t + ½ m Ec ( 2 Cos ωs t . Cos ωc t )
= Ec Cos ωc t + ½ m Ec [ Cos (ωs + ωc) t + Cos (ωs - ωc) t ]
( ) ( )-2 2
c cc c c c s c s
mE mEe E Cosw t Cos w w t Cos w w t= + + +
=Carrier Wave + Upper sideband wave + Lower sideband wave
(i). The AM wave is equivalent to the summation of three sinusoidal waves; one having amplitude Ec
and frequency fc, the second having amplitude (mEc/2 )and frequency (fc + fs) and the third having
amplitude (mEc/2) and frequency ( fc - fs).
(ii) The three frequencies of the AM wave fc, (fc + fs) and (fc – fs) are carrier frequency and other
two new frequencies are termed as ‘sideband frequencies’.
(iii) The sum of carrier frequency and signal frequency i.e. (fc + fs) is called upper sideband
frequency and frequency (fc – fs) is called lower sideband frequency.
Band Width = (fc + fs) - (fc – fs)
= 2 fs
Different Stages of Detection:
(i) Amplified modulated waves are received through antenna.
(ii) Amplified modulated wave thus received is rectified through a circuit (say diode) to have
a form of wave as shown in the figure below.
Fig. III : Different Stages of Detection
( c )
( b )
( a )
24
(iii) The rectified output is also a modulated wave consisting audio signal and carrier. The
carrier portion has frequency much higher than the audio signal. This is eliminated
through a filter circuit. The output is shown in figure III (c) which is just audio signal.
Here the detection procedure ends. This signal is then amplified by an amplifier which drives a
speaker to have Sound Output.
The Amplitude Modulation waves have following limitations:
(i) Noisy reception
(ii) Low Power efficiency
(iii) Small operating range (signal can not be transmitted to a large distance)
(iv) Lack of audio quality
Super Heterodyne Radio Receiver
[ In the previous section we have discussed about a straight radio receiver. The straight radio receiver
have the following limitations:
(i). In straight radio receiver for tuning to the desired station a variable capacitor is used. For this
selectivity of the tuning, circuit varies considerably which reduces sensitivity of the receiver.
(ii) To much interference is happened due to adjacent station ]
A Super Heterodyne Radio Receiver is free from these limitations.
Super Heterodyne Radio Receiver follows the steps given below:
(i). The radio waves from various broadcasting station are intercepted by the receiving aerial. The
desired frequency is tuned by tuning circuit. The signal is then amplified by the R.F. Amplifier up
to a desired level.
(ii) The amplified output of RF amplifier is fed to mixer stage where it is combined with the output of
a local oscillation. The two frequency beat together and produce an intermediate frequency (I.F.)
Intermediate Frequency = Oscillation Frequency - Radio frequency
R.F.
Amplifier Mixer I.F.
Amplifier Detector A.F.
Amplifier
Oscillator
Fig. IV : Block Diagram of a Super Heterodyne Receiver
455 KHz
25
(iii) The intermediate frequency is always 455 KHz and it is achieved by changing the oscillator
frequency simultaneously with the tuned carrier frequency. The Intermediate Frequency (I.F.)
is tuned to a single frequency 455 KHz which renders nice amplification to the desired level.
(iv) The output of the I.F. amplifier is fed to the Detector Stage. Here the audio signal is extracted
from I.F. output. [usually, diode detection circuit is used because of its low distortion and
excellent audio fidelity.]
(v) The audio signal output of detector stage fed to a multistage audio amplifier. Here, the audio
signal is amplified until it is sufficiently strong to drive the speaker.
ADVANTAGES OF SUPER HETERODYNE CIRCUIT
1. High R.F. Amplification: The super Heterodyne circuit produces an intermediate
frequency (455 KHz) which is much less than the radio frequency. At this frequency amplifier shows
much stability.
2. Improved Selectivity: Losses in tuned circuit are lower at I.F. this increases Q of tuned circuit
and this makes the amplifier circuit to operate with maximum selectivity.
3. Lower cost: In a super heterodyne circuit, a fixed R.F. amplifier is used. It also uses a fixed
frequency I.F. amplifier. The super heterodyne receiver is thus cheaper than other radio receivers.
26
Frequency Modulation
When the frequency of the carrier wave is changed in accordance with the intensity of the signal,
it is called frequency modulation.
In frequency modulation only the frequency of the carrier wave is changed in accordance to the
signal. However the amplitude of the modulated wave remains the same i.e. carrier wave amplitude. The
frequency variations of carrier wave depends upon the instantaneous amplitude of the signal as shown in
figure.
Advantages:
1. It gives noiseless reception.
2. The operating range is quite large.
3. More efficient
4. Fidelity is more.
5. Its operating range is quite large.
_____________
F.M. Wave
Carrier Wave
Signal
27
Propagation of Radio Waves
The propagation of Radio waves may be categorized into two forms:
I Ground Wave Propagation
a) Surface Wave Propagation b) Space Wave Propagation
II Sky wave Propagation
Surface Wave Propagation
Surface wave is part of the radio wave which travels along the surface of the earth. The wave is
supported at the lower edge by the ground. Such a propagation takes place when the transmitting and
receiving antenna are closed to the surface on the earth. Its importance is for medium and long wave
signals and specially during day time. For short distance surface wave propagation the curvature of earth
surface may be neglected and the field strength 0=s
E AE
d where E0 is unit distance field strength , d
is distance from transmitting antenna and A is a factor which takes into account the losses caused by the
earth.
E0 depends upon: i) Power radiated from the transmitting antenna.
ii) Directivity to the transmitting antenna in the vertical & horizontal planes.
A depends upon frequency, dielectric constant, conductivity of earth, distance from the transmitter
expressed is wave length .
For long distance surface wave propagation :
Up to 3
100
f Km, the formula used is 0=s
E AE
d
If the distance is more, the curvature of the earth is taken into account for the ground losses. The lower
the conductivity of the found the greater is the loss of field strength (Es). The higher the frequency
greater is the loss of field strength due to ground.
Space Wave Propagation:
The space is that part of the radio waves which travels from the transmitting antenna to receiving
antenna through the space, i.e. earths troposphere. This region of the earth’s atmosphere extends up to
15 Km from the earth’s
surface. The space wave is
constituted by two
components, namely the
direct wave and the ground
wave as shown in the figure.
[ Neglecting the curvature of
the earth and curvature of the
radio waves produced by the variation of refractive index of the earth’s atmosphere with height.]
Direct
Ground
Reflected
T R
HT HR
28
Space wave propagation is normally used for frequency between 30 to 60 MHz . Frequencies above
60MHz are never refracted back to the earth by the ionosphere and it is only under special circumstances
that frequencies in the range of 30 to 60 MHz are so returned. This surface wave is attenuate extremely
and rapidly. At this high frequency as a consequence communication at frequencies above 30 MHz is
possible only through space wave. Transmitting and receiving antenna are both at the earth surface, then
the two components of this space wave are equal in magnitude and opposite in phase, hence they
cancel each other at the receiving antenna leaving the surface wave as the only component of ground
wave This is the case of ground wave propagation and broadcast transmission. As the height of the
antenna expressed in wave length are increased, the amplitude of space wave increases rapidly and
when the height equals the eave length or few more, the space wave becomes the principle part of
ground wave. The magnitude of the space wave and surface wave are influenced by the following
factors:
1. Resistivity and dielectric constant of the earth (influence the rate of attenuation)
2. Frequency of the wave
3. Height HT and HR
4. distance ‘d’ between transmitting and receiving antenna
5. Variation of refractive index of earth’s atmosphere with height.
- Frequency of the radio wave determines the rate of attenuation of the surface wave.
- Height length ration and the wave of the two antenna: Higher the frequency, higher is
the rate of attenuation of the surface wave and higher is the height of each antenna
expressed in wave length. HT and HR determines the relative amplitude and phase of the
surface and space wave and hence influence the resultant field strength at the receiving
antenna. Curvature of earth also influence the phase and magnitude of surface and space
wave.
In general the transmission is possible only up to or slightly beyond the line of
sight distance, hence the factor which determines the range is
d2 + r
2 = ( r + h )
2
or d2 + r
2 = r
2 + h
2 + 2 r h
d2 = h
2 + 2 r h
Since h2 ‹‹ 2 r h, therefore neglected, thus we get
d = 2 r h or d = 1.23 h miles
Thus the service area increases on increasing the height of transmitting
and receiving antenna.
Sky wave (Ionosphere) Propagation
Radio wave is short wave range, radiated from antenna at large angle with the ground, traveled
through the atmosphere and encounter the ionized region of the upper atmosphere under favourable
circumstances, the radio waves get bend downward due to refraction from different parts of the ionized
29
region and again reach the earth at a far distant point. Such a radio wave is called sky wave and such a
propagation is termed as sky wave Ionospheric propagation. Long distance propagation is by sky wave
Ionosphere:
By Ionosphere, it is meant that the upper part of the
atmosphere where ionization is appreciable. This upper parts of the
earth’s atmosphere absorbs large amount of radiant energy from the
sun. This heats the atmosphere and also cause ionization resulting in
free electron and positive and negative ions. This ionization is stratified because of difference in the
chemical composition and physical properties of the atmosphere at different heights and also because of
unequal abilities of different gases in absorption solar radiation of different frequencies.
This figure gives the variation of electron density with height for during day and during night time.
The seasonal variation with the height also take place (virtual height). The virtual height of an
Ionospheric layer is the height to which a short pulse of energy sent vertically upward and traveling with
the speed of light would reach taking the same two way travel time as does the actual pulse reflected
from the layer. The virtual height is greater than true height of reflection because the velocity of
propagation I the ionized layer gets reduced below the velocity of light due to interchange of energy
between the wave and the electron of ionized layer. This difference is very small and it depends on the
distribution of electron in the layer. The virtual height of E, F1 & F2 also undergo diurnal and seasonal
variation.
Critical Frequency: Critical frequency of the ionized layer is the highest frequency that is reflected by
the layer at vertical incidence. Critical frequency is proportional to the square root of the maximum
electron density of the layer.
F ξ∝ Where ξ is maximum electron density.
This also undergoes the diurnal and seasonal variation.
F2 Layer
F1 Layer
E Layer
D Layer
50 to 90 Km
110 Km
220 Km
250 to 300 Km
F2 Layer
E Layer
Electron Density (During Day) Electron Density (During Night)
30
Skip Distance:
Critical frequency is the maximum frequency of the radio wave which is returned from a layer for
normal incidence. In case the frequency of Radio wave exceeds the critical frequency, the influence of
Ionospheric layer on path of propagation depends upon the angle of incidence at the ionosphere with a
large value of angle of incidence Øo such as for ray R1
µm = Sin Øo is satisfied when µm < 1 i.e. electron density is small. In such case the radio
wave is returned earthward after having penetrated only slight distance into the ionized layer. As the
angle of incidence Øo is progressively decreased for rays R2 and R3, the refractive index for returning the
wave earthwards progressively decreased for rays R2 and R3, the refractive index required for returning
the wave earthwards progressively decreases and the penetration to layer increases.
If the angle Øo is reduced so much that Sin Øo becomes less than µm ( Sin Øo < µm ),
corresponding to the maximum electron density in the layer, then radio wave penetrates through layer as
R5 and R6.
Ionosphere
Earth
Direct
Ground
Reflected
Satellite
Sky Wave
Space Wave
Wave Propagation
[ various modes ]
31
It may be seen that if angle of incidence is progressively reduced the distance from the
transmitting antenna at which
the radio waves re-strikes the
found decreases until it reaches
the minimum value and then it
again increases with further
decrease of angle of incidence
Øo , such as for ray R4. The
maximum distance from the
transmitter at which a sky wave
of a given frequency is returned
to the earth by the ionosphere is
called Skip distance.
Ray R4 reaches a
distant point on the ground taking a longer route and having traveled most horizontal for a considerable
distance.
Within Skip distance no signal is received.
For short wave, the ground waves die out rapidly with distance where as sky wave returns to
ground skipping return distance.
Skip distance depends upon
1. Frequency of transmission i.e. more the frequency, more is the skip distance.
2. Critical frequency of Ionospheric layer.
3. Height of layer (ionized layer)
4. Distribution of ionization within the layer.
Maximum Usable Frequency [ MUF ]
At a fixed receiving point at any particular time, there is a maximum frequency which may be
used without letting the sky wave to skip over the receiving point. This is called Maximum Usable
Frequency.
1. For fixed location MUF = 1, which makes a distance to receiving point equal to the skip
distance.
2. MUF is the highest frequency that can be used to receive Sky wave signals at receiving
point.
3. MUF is the frequency that in general gives strongest signal also.
_________________
R5R6
Ionized Layer
Region for Maximum
ionized density
Skip Distance
R4
R3 R1
R2
Travel of Radio Waves at different angles of Incidence
Electric Current & Ohm’s Law Electric Current (I)
• It is the rate of flow of electric charge flowingthough any section of wire.
• • Unit of current is Ampere (A).• One ampere of current flows in a wire when one
coulomb of charge flows through the wire in onesecond.
Electric Current in a ConductorThe electrons in a conductor move due to thermal motion during which they collide with the fixed ions.
• The direction of its velocity after the collision iscompletely random. At a given time, there is nopreferential direction for the velocities of theelectrons. Therefore, there will be no netcurrent.
• Electrons in a conductor move under the actionof the electric field applied across its two ends.
Ohm’s Law
• Electric current flowing through a conductor isdirectly proportional to the potential difference acrossthe two ends of the conductor; physical quantitiessuch as temperature, mechanical strain, etc.remaining constant.
V∝ I
•
V − I graph for an ohmic conductor
V = RI
Where, R is resistance of the conductor
• SI unit of resistance is ohm.Resistance of a conductor depends on:
o Length of the conductor (l)o Area of cross-section (A) of the
conductor
ρ is the electrical resistivity of the conductor.
• Using Ohm’s law,
is current per unit area, also called current density (J).
Let E be applied electric field across the conductor.
∴V = E l ……. (iii)
From equations (i), (ii), and (iii),
El = Jρl
E = Jρ
Where, is called the conductivity (σ)
Drift of Electrons & Limitations of Ohms Law
Free electrons are in continuous random motion. They undergo change in direction at each collision and the thermal velocities are randomly distributed in all directions.
∴ Average thermal velocity,
is zero … (1)
•
The electric field E exerts an electrostatic force ‘−Ee’.
Acceleration of each electron is,
Where,
m → Mass of an electron
e→ Charge on an electron
• Drift velocity − It is the velocity with which freeelectrons get drifted towards the positiveterminal under the effect of the applied electricfield.
Where,
Thermal velocities of the electrons
Velocity acquired by electrons
τ1, τ 2 → Time elapsed after the collision
Since = 0,
∴vd= a τ
Where, is the average time elapsed
Substituting for a from equation (2),
•
Electron drift to a small distance in a time Δt = VdΔt
Amount of charge passing through the area A in time Δt ,q = IΔt
IΔt = neAvdΔt
Where,n→ Number of free electrons per unit volume
From equation (4),
Current density (J)
We know,
J = σ E
Mobility (μ)
• It is defined as the magnitude of the driftvelocity per unit electric field.
• Unit of mobility is m2/Vs.
•
Limitations of Ohm’s Law
There are several materials and devices for which the proportionality of V and I are as follows:
• V ceases to be proportional to I.
• Sign of V affects the relation between V and I.
• There is more than one value of V for the samecurrent.
Example − GaAs
Resistivity of Various Materials
• Metals have low resistivities. It is in the range of10−8 Ω m to 10−6 Ω m. Insulators haveresistivities 1018 times greater than metals.Semi-conductors lie in between them.
• Resistors are of two types:
• Wire bound resistor
• Carbon resistor• Carbon resistors are extremely small in size.
Therefore, their values are given using a colourcode.
TABLE of RESISTOR COLOUR CODES
Colour Number Multiplier Tolerance (%)
Black 0 1 -
Brown 1 101 -
Red 2 102 -
Orange 3 103 -
Yellow 4 104 -
Green 5 105 -
Blue 6 106 -
Violet 7 107 -
Gray 8 108 -
White 9 109 -
Gold - 10−1 5
Silver - 10−2 10
No colour - - 20
• Here, first two bands from one end indicate thefirst two significant figures of resistance inohms.
• Third band indicates the decimal multiplier.• The last band stands for tolerance. Its absence
indicates a tolerance of 20%.
Temperature Dependence of Resistivity
For Metallic conductor
In terms of relaxation time, the resistivity of the material of a conductor is given by,
Where, the letters have their usual meanings
If the temperature increases, the amplitude of the vibrations of the +ve ions in the conductor also increases. Due to this, the free electrons collide more frequently with the vibrating ions and as a result, the average relaxation time decreases. Since ρ ∝ 1/τ, the resistivity of a metallic conductor increases with increase in temperature.
• Resistivity of a metallic conductor is given by,
ρT = ρ0 [1 + α (T − T0)]
Where,
ρT→ Resistivity at temperature T
ρ0 → Resistivity at reference temperature T0
α → Temperature co-efficient of resistivity
• α is + ve for metals.• Graph of ρTplotted against T should be a straight
line. At temperature lower than 0°C, the graphdeviates from a straight line.
For Alloys
In case of an alloy, the resistivity is very large and it has very weakdependence on temperature.
• Nichrome (an alloy) exhibits weak dependenceof resistivity with temperature.
For Semi-conductors
• Resistivity of a semi-conductor decreases withtemperature.
Electric Energy & Power & Combination of resistors
Electric Energy
Work done by the source of emf in maintaining the electric current in the circuit for a given time is called electric energy consumed in the circuit.
V = IR
q = It
W =Vq
∴W= VIt
Where,
V → Potential difference
I → Current
R → Resistance
q → Charge
t → Time
W → Work done
• V is in volt, I in ampere, and t in seconds. Theenergy dissipated is in Joule.
Electric Power
• Itis the rate at which work is done by the source of emf in maintaining the electric current in a circuit.
Where,W → Work done , t → Time
P → Electric power
• SI unit of power is watt.
• Expression of electric power in terms ofV and I
P = VI
• I and R----------------- P = I2R
• V and R----------------
Combination of resistors
Resistors in Series
• Two or more resistors are said to be connectedin series, if same current passes through each ofthem, when a potential difference is appliedacross them.
Equivalent resistance, RS = R1 + R2 + R3
Resistors in Parallel
• Two or more resistors are said to be connected in parallel, if potential difference across each of them is equal to the applied potential difference.
• Equivalent resistance (RP)
Cell & Combination of Cells
Emf
• Potential difference between the two poles of the cell in an open circuit is called emf of the cell.
SI unit is volt (V).
Internal resistance (r) of cell
• Resistance offered by the electrolyte of the cell when the electric current flows through it
E − emf of cell
r − Internal resistance of the cell
R − External resistance
K − Key
V − Voltmeter
• The key K is closed and a current I flows in the circuit.
According to Ohm’s law,
• Let V be the terminal potential difference. The terminal potential difference V is less than emf E of the cell by an equal amount, which is equal to potential drop across external resistance R i.e.,
∴V = E − Ir
Also, terminal potential difference is equal to potential differences across external resistance.
V = IR
From equation (1),
Combination of cells
Cells in Series
E1E2 − emf of two cells
r1, r2 − Internal resistance of two cells
I − Current in the circuit
Terminal potential difference across the first cell, V1 = E1 − Ir1
Terminal potential difference across the second cell, V2 = E2 − Ir2
Potential difference between the points A and B,
V = V1 + V2 = (E1 − Ir1) + (E2 − Ir2)
= (E1 + E2) − I (r1 + r2)
Let
E − Effective emf
r − Effective internal resistance
V = E − Ir
∴E = E1 + E2
R = r1 + r2
• Current in the circuit,
• If the two cells are connected in opposite direction, then
E = E1 − E2
Cell in Parallel
E1, E2 − emf of two cells
r1, r2 − Internal resistances of cell
I1, I2 − Current due to the two cells
Terminal potential difference across the first cell,
V = E1 − I1r1
For the second cell,
Let E is effective emf and r is effective internal resistance.
V = E − Ir
And,
Kirchhoffs Rules, Wheatstone Bridge& Meter Bridge
Kirchhoff’s First Law − Junction Rule
• The algebraic sum of the currents meeting at a point in an electrical circuit is always zero.
I1, I2I3, and I4
Convention: Current towards the junction – positive Current away from the junction − negative
I3 + (− I1) + (− I2) + (− I4) = 0
Kirchhoff’s Second Law − Loop Rule
• In a closed loop, the algebraic sum of the emfs is equal to the algebraic sum of the products of the resistances and current flowing through them.
For closed part ABCA,
E1 − E2 = I1R1 + I2 R2 − I3R3
For closed part ACDA,
E2 = I3R3 + I4R4 + I5R5
NCERT :- (a) Junction rule: At any junction, the sum of the currents entering the junction is equal to the sum of currents leaving the junction . This applies equally well if instead of a junction of several lines, we consider a point in a line. The proof of this rule follows from the fact that
when currents are steady, there is no accumulation of charges at any junction or at any point in a line. Thus, the total current flowing in, (which is the rate at which charge flows into the junction), must equal the total current flowing out. (b) Loop rule: The algebraic sum of changes in potential around any closed loop involving resistors and cells in the loop is zero. This rule is also obvious, since electric potential is dependent on the location of the point. Thus starting with any point if we come back to the same point, the total change must be zero. In a closed
loop, we do come back to the starting point and hence the rule.
Wheatstone Bridge
• R1, R2, R3,and R4 are the four resistances. • Galvanometer (G) has a current Ig flowing
through it at balanced condition,
Ig = 0
• Applying junction rule at B,
∴I2 = I4
• Applying junction rule at D,
∴ I1 = I3
• Applying loop rule to closed loop ADBA,
• Applying loop rule to closed loop CBDC,
From equations (1) and (2),
(Balanced condition)
• For a balanced bridge, the unknown resistance can be determined as:
Metre Bridge
• Consists of a 1 m long wire of uniform cross-section
• Construction of the metre bridge is shown in the above figure.
• Let R − Unknown resistance
S − Standard resistance
l1 − Distanc e from A
Rcm − Resistance of the wire per unit centimetre
Rcml1 − Resistance of length AD
Rcm (100 − l1) − Resistance of length DC
• From the figure, the balance condition gives
Potentiometer
Principle
When a constant current is passed through a wire of uniform area of cross-section, the potential drop across any portion of the wire is directly proportional to the length of that portion.
Construction
• Consists of a number of segments of wire of uniform area of cross-section
• Small vertical portions are made of thick metal strip connecting the various sections of wire.
• A rheostat is connected to the circuit, which can vary the amount of current flowing in the wire.
Applications of Potentiometer
• Comparison of emf of two cells
• E1, E2 are the emf of the two cells. • 1, 2, 3 form a two way key. • When 1 and 3 are connected, E1 is connected to
the galvanometer (G). • Jokey is moved to N1, which is at a distance l1
from A, to find the balancing length. • Applying loop rule to AN1G31A,
Φ l1 + 0 − E1 = 0 (1)
Where, Φ is the potential drop per unit length
• Similarly, for E2 balanced against l2 (AN2),
Φ l2 + 0 −E2 = 0 (2)
• From equations (1) and (2),
• Measures internal resistance of a cell
• The cell of emfE (internal resistance r) is connected across a resistance box (R) through key K2.
• K2 − open, balance length is obtained at length AN1 = l1
E= Φ l1 (3)
• K2 − closed • Let V be the terminal potential difference of cell
and the balance is obtained at AN2 = l2
∴V = Φ l2 (4)
From equations (3) and (4),
•
From (5) and (6),
