Symbols

Simple Circuits

• A complete circuit is needed for a current to flow.

• A current is a flow of electrons which move from the –ve terminal of the power supply to the +ve. In Physics, however, we still show the current flow from +ve to –ve.

• The electrons are called charge carriers.

Electron Flow In Circuits

In a metal some electrons are released from each atom, and so are free to move about.

Metal Ions (+ve)

Electrons (-ve)With no voltage the electrons do not move in any particular direction.

Metal Conductor

Metal Conductor

Metal Ions (+ve)

Electrons

+ve -ve

When a Potential Difference (PD) is applied all the electrons move in the same direction.

•Metals contain at least 1 free electron per atom. The e’s move at random when no current flows leaving behind a positive ion.

• When a power supply is connected to a metal wire the e’s are attracted to the +ve terminal. They collide with the +ve ions which slows them down. The wire therefore has a certain amount of resistance.

• The e’s gain energy from the power supply and give it to the ions when they collide. This is why a metal gets hotter whenever a current flows.

• Charge can be carried by other charge carriers like ions and not just electrons. e.g.salty water will conduct a small current

• Insulators do not have any free electrons i.e. no conduction.

Charge and Current

• Current is the rate of flow of charge. For a current, I, the charge flow, ΔQ, for a time, Δt, is given by:

• I = ΔQ

Δ t• OR ΔQ = IΔt• e.g. Q How much charge flows when there is a

current of 2A for 10 minutes • A ΔQ = I Δt• =2A x 10 x 60• = 1200C (coulombs)

• The charge on 1 electron is -1.6x10-19C so we can find the number of e’s flowing by dividing the charge in C by the charge on 1 electron.

• e.g. -1200C

-1.6 x 10-19C

• = 7.50 x 1021 electrons

Electrical power and Energy

• The power supply does work in pushing the electrons around the circuit.

• The voltage across the power supply is called the e.m.f. (electromotive force).

• Whenever work is done there is a transfer of energy and the power supply gives energy to the circuit.

•Definition of voltage or potential difference:

• The p.d. between 2 points is the work done per coulomb of charge moving between the 2 points.

• P.d = work or V = W

• charge Q

• Or 1V = 1JC-1

• Similarly, if the e.m.f. is 1.5V, then the power supply gives 1.5J of energy to each coulomb of charge.

• Re-arranging the equation V = W Q

• gives W = QVor W = ItV

• Remember W = work done = energy transferred• Power is the rate of doing work or the rate of

transfer of energy.• P =W = E t t• Substituting for W gives

P = ItV = IV t• Power is measured in watts (W)

Resistance

• Resistance is the opposition to current flow. It is caused by collisions between the electrons and positive ions.

• Resistance = p.d. across component• current through component • R = V or V = IR

I• Resistance is measured in ohms (Ω)

Digital Multimeter

Measuring current

• We measure current using an ammeter placed in series in the circuit.

• A perfect ammeter would have zero resistance so that it does not alter the size of the current that it is measuring.

• All connecting leads should also have zero resistance.

Measuring p.d.

• A voltmeter is used to measure the voltage or potential difference (p.d.) across a component.

• A voltmeter is always connected in parallel with the component.

• A voltmeter should have a very high resistance so that it does not take any current from the circuit.

Measuring resistance

• Connect up the circuit shown in fig.1 on P51

• Use the variable resistor to obtain 7 pairs of readings of current and p.d.

• Plot a graph of p.d. against current • Sine V = IR the gradient of this graph

gives the resistance.• Resistance can also be measured directly

with an ohm-meter.

Resistivity

• Long wires have more resistance than short wires• Thin wires have more resistance than thick wires.• Different types of wire have different resistance.• We can calculate the resistance of a wire using

Resistance = resistivity x length X- sectional area

R = ρl A

• Definition: ρ = RA = resistance x area• l length• Resistivity is a property of the material whereas

resistance is a property of the component.

See the table on P.52 for the resistivities of various materials.

• Metals have a low resistivity and insulators have a high resistivity. Semi-conductors are somewhere in the middle.

• The units for resistivity are Ωm.

Example• Find the resistance of a 50cm length of

copper wire with a cross sectional area of 1 x 10-6m2

• R = ρl

• A

• = 1.7 x 10-8 x 0.5

• 1 x 10-6

• = 8.5 x 10-3Ω

Superconductivity

• Some materials lose all their resistance below a certain critical temperature. e.g. mercury has no resistance below -269°C.

• Superconducting wires do not become hot, because electrons can flow through them without any transfer of energy. This is useful for power lines.

• Very strong electromagnets can also be made using superconductors.

Controlling Voltage and current

• A rheostat or variable resistor in series with a component can control the current through it.

• A rheostat has a maximum resistance so it cannot reduce the current to zero.

Potential Divider• A rheostat can be used as a potential

divider.

• As the sliding contact moves from one end to the other, the output increases from 0 –max. i.e. any fraction of the whole voltage can be obtained.

Supplying a variable voltage• We now have 3 methods for supplying a

variable voltage:• A variable resistor in series with the power

supply• A variable power supply. (e.g our black

supplies but they will only supply a small current).

• A fixed power supply with a rheostat connected to it as in the potential divider circuit.

I-V Graphs

• Set up the circuit shown in fig.2(a) on P 53 and use the potential divider circuit to obtain 7 pairs of values of current and p.d. for a resistor, lamp and diode for both positive and negative values of p.d.

• Plot a graph of current against p.d. fpr each one.

• You can aslo do this using sensors.

Graphs

I – V Graphs• For a fixed resistor the graph is a straight line

through the origin.• Current is directly proportional to voltage • This is called Ohm’s law and applies to many

resistors and metals at constant temperature. Such components are described as ohmic conductors.

• For a lamp the graph is not a straight line through the origin so Ohms law is not obeyed.

• Lamps get hotter as the current increases. This causes an increase in its resistance and the I-V graph becomes less steep. i.e. as the p.d increases the current increases by smaller amounts

• The diode allows current to flow in one direction only. This is called the forward direction. The current increases dramatically once a certain voltage has been reached.

• Very little current flows in the reverse direction. It has a very high resistance in this direction.

Change of Resistance• The resistance of a metal increases with

temperature. It has a positive temperature coefficient

• A rise in temperature causes an increase in the vibrations of the +ve ions so the e’s collide more frequently.

Thermistors• As the temperature increases the resistance of

the thermistor decreases and the current therefore increases

• A thermistor can be used to make a thermometer by calibrating a milliammeter in ºC instead of mA when connected in series with the thermistor

• Since the resistance of a thermistor decreases as the temperature increases we say it has a negative temperature coefficient

• Semi-conductors have covalent bonds joining atoms together. As the temperature rises more e’s are released as these bonds break. Since there are more charge carriers, the current increases.

• Thermistors are therefore used in temperature sensitive devices.

Current in series circuits• In a series circuit:

• The current is the same size all the way round the circuit.

• The size of the current depends upon the supply voltage and the amount of resistance in the circuit

Currents in Parallel circuits

• The sum of the currents entering any point in a circuit is equal to the sum of the currents leaving that point. (This is called

Kirchhoff’s 1st Law)

• The current through each branch of a parallel circuit depends on the resistance of that branch and is independent of the other branches.

Potential Difference in Series Circuits

The e.m.f of the battery in a series circuit is equal to the

sum of the potential differences across the

components

V1 = V2 + V3

Parallel circuits

The voltage (potential difference) across each

branch in a parallel circuit is equal to the e.m.f. of the

battery.

V1 = V2 = V3

Think!

• Two different light bulbs are connected in series to the same power supply. Explain why one glows brighter than the other

Resistors in series and in parallel

• See P.61-62 for proofs of these formulae that you are given.

• For resistors in series, Rt = R1+ R2

• For resistors in parallel,

• If there are n resistors in parallel and they each have resistance R then Rt = R

n

21

111

RRRt

Calculating Power from Resistance• When current flows through a resistor, work is done on the resistor and it gets hot. e.g. in an electric iron

• The rate of doing work or power is given by P=IV = I(IR)

• i.e. P = I2R (GIVEN)• This gives the rate at which heat energy is

transferred to the surroundings.

EMF and Internal Resistance

• Connect a voltmeter across the terminals of a cell and record the reading.• This is called the terminal p.d. • This is also the e.m.f of the cell. The e.m.f.

gives the total work done per coulomb of charge that flows around the circuit.

ε = Wt

Q

• Now connect up to 3 lamps in parallel and note the reading on the voltmeter.

• The terminal p.d. falls as current is drawn from the cell. The difference between the e.m.f. and the terminal p.d. is called the lost volts.

• This is because some p.d. is being used to drive the current through the cell itself. The cell has internal resistance.

• Definition: Internal resistance is the resistance to flow of current inside the cell itself.

• The emf of a cell in any series circuit = sum of the p.d.’s around the circuit

• i.e. emf of cell = terminal p.d. + “lost volts”• ε = V + v• If a cell of emf, ε, with internal resistance, r, is connected to an external resistor, R, then:• ε = IR + Ir• This can also be written as ε = V +Ir• OR ε = I(R + r)

• Rearranging gives V = ε – Ir (Given)

• We can rewrite this as V = -Ir + ε

V = -rI + ε

• The equation of a straight line is y= mx + c

• so if we plot a graph of V against I then:

• The line is a straight line with a negative gradient.

• The gradient = internal resistance

• The intercept give the e.m.f of the cell. i.e the emf = p.d at zero current

Electrical Power• Since ε = IR + Ir• We can multiply by I to give:• Iε = I 2R + I 2r• i.e. power supplied by cell = power

delivered to the external resistor, R + power wasted in cell due to its internal resistance

• The graph on P 65 shows that the power delivered to a resistor, R (the load) is a maximum when R = r

Effects of Internal Resistance

• When a cell is short circuited r is the only resistance.

• For a 1.5V dry cell r = 0.5Ω and I = 3A• Rechargeable cells have a very low

internal resistance so I can be dangerously large.

• In any circuit if R = 0, then I = ε and r r

limits the size of the current

Car batteries and E.H.T.Power supplies

• Car batteries and low voltage power supplies have a very low internal resistance so they can provide a large current.

• An E.H.T. power supply has a very large internal resistance to limit the current it supplies to a safe value.

Cells in series

• When cells are connected in series the total emf = sum of emf’s and the total resistance = sum of internal resistances

• e.g. 4 cells of emf, 1.5V and internal resistance, 1Ω have a total emf of 6V and total internal resistance of 4Ω

Cells in parallel

• When cells are connected in parallel the emf is the same as for one cell i.e ε

• If the internal resistance of each cell is r, then they must be combined together in parallel so if there are n cells then the total internal resistance = r

n• e.g If there are 4 cells of emf 1.5V and

internal resistance, 4Ω then the total emf = 1.5V and the internal resistance = 1Ω

The Potential divider

• Using a chain of resistors as shown in fig 1 on P70 we can see how the p.d. from a source can be divided in proportion to the resistances.

• We have already seen when plotting the

I-V graphs how a variable resistor can be used to give any fraction of the maximum p.d from a power supply.

Other uses of a potential divider• As an audio “volume control”. The cell in

the potential divider circuit is replaved with the audio signal p.d. The variable output is then supplied to a loudspeaker.

• In a dimmer switch to vary the brightness of a lamp from zero to a maximum

Light sensitive potential divider

• Set up the circuit shown in fig 4 on P71.• As the light intensity increases the

resistance of the LDR decreases and the voltage across it decreases. The output decreases.

• If the variable resistor and LDR are then swapped the output p.d. increases as the light intensity increases and the circuit can be used as a light meter.

Temperature Sensitive Potential Divider

• Set up the circuit shown in fig 4 on P71.• As the temperature increases the

resistance of the thermistor decreases and the p.d decreases.

• If the varaiable resistor and thermistor are swapped round the output p.d. increases as the temperature rises. The circuit could be used to operate an alarm if the temperature becomes too high.

Alternating currents

• Direct current from a battery moves in one direction only, from positive to negative.

• In alternating current the direction is changing all the time. The charge carriers are moving forwards and backwards many times a second. In Europe it is 50 Hz (cycles per second)

• AC and DC are equally good at heating, lighting, or running motors.

• This graph shows the difference between d.c. and a.c.

•

• One complete alternation is called a cycle.

• The frequency is the number of cycles per second.  Units are hertz (Hz).

• The period is the time taken for one cycle.  It is measured in seconds.  f = 1/T.

• The current follows exactly the same wave form as voltage.

• The graph is called a sinusoidal waveform or a sine wave.

Peak values

• The peak value of current or p.d. is the maximum value of current or p.d.

• The peak value can be found from the amplitude of the wave.

• The peak-to-peak value = 2 x peak value

• e.g. If the peak value is 300V then the peak-to-peak value is 600V

Root-mean square (r.m.s.) values

• This is the value of direct current which has the same heating effect as the alternating current in the same resistor.

Calculating rms values

• The proof on P76 shows that the rms values of current or p.d. = 1 x peak value

√2

• If the peak current = Io and the peak p.d. = V0

• then

Example

• Q The rms value of the mains in the UK is 230V. Calculate the peak value and the peak-to-peak value

• A Vo = √2 x Vrms

• = √2 x 230

• = 325V

• Peak-to-peak = 650V

Calculating Power

• For dc, power = current x voltage

• For ac, the peak power = I0 x Vo

• The power varies between I0Vo and zero

• Average power = I0 x Vo = I0 x Vo = Irms x Vrms

• 2 √2 √2

Oscilloscopes

Oscilloscopes• Inside the oscilloscope there is a beam of

electrons which hit the screen to produce a dot.

• This dot can be made to move across the screen at different speeds by adjusting the time base.

• If it is moving fast enough a straight line is produced.

• The dot/line can also be made to move up/down by connecting a signal to the y-input.

Uses

• An oscilloscope is connected in exactly the same way as a voltmeter, i.e. in parallel with a component. (The input resistance is very high)

• An oscilloscope can be used as a DC voltmeter. We get a horizontal line or a dot, depending whether the time base is on. If it is used as an AC voltmeter, it will show the sinusoidal waveform

Controls• The most important controls that we use are: • The y-gain setting, calibrated in Vcm-1. • The time base, in scm-1. •  We measure the voltage on the vertical  axis. 

We can adjust the sensitivity by turning the knob marked y-gain.

• The horizontal direction is determined by the time base setting.   We can change this by using the time base knob.

Example using ac

• Q The time base is set at• 2 mscm-1 and the• y gain at 0.5 Vcm-1

• (a) What is the peak to peak voltage?• (b) What is the peak voltage?• (c) What is the rms voltage?• (d)  What is the period?• (e)  What is the frequency?

Answers• (a) The total height of the wave from peak to

trough is 6.4 cm So Vpk-to-pk = 3.2 V

• (b) Vpk = 3.2/2 = 1.6 V

• (c)   Vrms = Vpk /2 = 1.6 /2 = 1.13 V

• (d) 1 cycle is 2.9 cm

• Time period = 2.9 2 = 5.8 ms = 5.8 10-3 s (e) f = 1/T = 1/5.8 10-3 = 178 Hz

Examples using dc• 1. using a d.c source with the time base on

___________

• __________

• p.d. = 0 p.d. = 0.5V

• Using y-gain setting the input voltage can be found.

3. Pulse followed by echo

• The time between a pulse of current and its echo can be found directly using the time base setting. See fig4 on P78