C20 ~ Kirchhoff's Laws

Reorganized by mr itune jk 0724682620 gk phy

Industrial mathematics SPH 2131

C20 ~ Kirchhoff’s Laws

Objective: To verify Kirchhoff’s Laws by comparing voltages and currents obtained from a real circuit to those Predicted by Kirchhoff’s Laws. Introduction: A simple circuit is one that can be reduced to an equivalent circuit containing a single resistance and a single voltage source. Many circuits are not simple and require the use of Kirchhoff’s Laws to determine voltage, current, or resistance values. Kirchhoff’s Laws for current and voltage are given by equations 1 and 2. In this experiment, we will construct two circuits with 4 resistors and a voltage source. These circuits will not be simple, thus Kirchhoff’s Laws will be required to determine the current in each resistor. We will then use a digital multi-meter to obtain an experimental value for the voltage across each resistor in the circuits. Kirchhoff’s Laws will then be applied to the circuits to obtain theoretical values for the current in each resistor. By applying Ohm’s Law, we can then obtain a theoretical value for the voltage across each resistor. The experimental and theoretical voltages can then be compared by means of % error.

Equation 1: Σ junction I=0 junction law

Equation 1: Σ loop I=0 loop law Equipment: Proto-board 4 resistors: (R1=68kΩ, R2=47kΩ, R3=15kΩ, R4=1000kΩ) Digital multi-meter Variable power supply Wire leads and alligator clips Experimental Procedure Part 1: figure 1 1. Using the proto-board, the 4 resistors, the variable power supply, and the wire leads and alligator clips; construct the circuit shown in Figure 1. First ascertain the values of the resistance of the resistor. 2. Turn on the power supply. Connect the multi-meter across the power supply and adjust the voltage to suitable D.C. voltages {Get guidance from the lab INSTRUCTOR} 3. Connect the multi-meter across each of the 4 resistors Put the multi-meter in series to each resistor and record the current through each. Record these 4 values of voltage and current in the data table. 4. Turn the power supply off and disconnect the circuit. Experimental Procedure Part 2: figure 2 1. Add a second power supply to the circuit as shown in Figure 2. 2. Turn on the power supplies. Adjust the voltages V1 and V2 to 4.0 volts. 3. Connect the multi-meter across each of the 4 resistors Put the multi-meter in series to each resistor and record the current through each. Record these 4 values of voltage and current in the data table. 4. Turn the power supply off and disconnect the circuit. Analysis: 1. For the first circuit, use equations 1 and 2 to write a system of linear equations that may be solved for the current in each branch of the circuit. Then, solve the system to obtain a theoretical value for each current. Show your work! 2. Using the currents obtained in step 1 of the analysis; apply Ohm’s Law to determine the theoretical voltage across each resistor. 3. Compare the theoretical voltages obtained in step 2 of the analysis to those measured in the actual circuit in Figures 2 and 1. 4. Repeat steps 1 to 3 for the second circuit. 5. Record the theoretical voltages, the experimental voltages, and the % errors in the results table. Challenge: figure 3 Repeat experimental steps 1-4 and the analysis for the circuit in Figure 3 with resistors and a power supply: (R1=68kΩ, R2=47kΩ, R3=22kΩ, R4=15kΩ, R5=1000kΩ)


I12

C

I7

I8

I9

R1

R2

R3 R4

V

R1

R2

R3 R4

Vx

Vy

R1

R2

R3 R4

Vz

R5

B

I4

I5

I6

A

I1

I2

I3

D

I10

I11

E

G

F

H

Figure 1

Figure 2

Figure 3

Reorganized by mr itune jk 0724682620 gk phy Table of results:

Figure 1 V (theoretical) V (experimental) Percent error

R1

R2

R3

R4

Figure 1 I (theoretical) I (experimental) Percent error

R1 I2 = I2 =

R2 I2 = I2 =

R3 I1 = I1 =

R4 I3 = I3 =


R1

R2

R3

R4


R1 I5 = I5 =

R2 I5 = I5 =

R3 I4 = I4 =

R4 I6 = I6 =



R1

R2

R3

R4

R5


R1 I8 = I8 =

R2 I12 = I12 =

R3 I11 = I11 =

R4 I9 = I9 =

R5 I10 = I10 =

Now get the summation,Σ, of currents at the following junction:

At junction A, Σ (I1,I2,I3)=

At junction B, Σ (I4,I5,I6)=

At junctionC, Σ (I7,I8,I9)=

At junctionD , Σ (I11,I10,I7)=

At junction E, Σ (I10,I12,I8)=

At junction F, Σ (I11,I9,I12)=

At junction G, Σ (I4,I5,I6)=

At junction H, Σ (I1,I2,I3)=

now solve for v, vx, vy, vz and vw using appropriates loops.

measure the actual input voltages and account for the difference. Is the kirchoffs law verified? Comment and reccommend


W4 THE RIPPLE TANK

AIMS: The aims of this experiment are:

1. To observe the characteristics and behavior of water waves.

2. To show the analogy between water waves and light waves.

APPARATUS

Water ripple tank, Metal reflectors , Low voltage power unit (3.0 V D-C) ,Ammeter ,Variable resistor, Motor

Vibrator, Lamp, Level.

INTRODUCTION

The ripple tank is an apparatus for studying the phenomena of water waves. The wave generator is a vibrator set

into motion by a 3V.D.C Motor. A variable resistor in series with the motor varies its speed and therefore the

frequency of vibrations. A lamp illuminates the wave pattern. The wave pattern is projected on the table through

the transparent bottom of tank. If one wishes to copy a wave pattern on paper the paper can be spread out on the

table under the ripple tank. When measuring wavelengths or other distances remember to measure these lengths

as they are in the ripple tank. For calibration place an object of known length on the bottom of the ripple tank

and measure the length of its image.The ripple tank should be leveled using the spirit level. Use so much water

that it stands midways on the sloping walls. The wave generator with wooden plate and motor has to be raised

or lowered so that the wave source just touches the water surface. The wave pattern can be ‘stopped’ by viewing

through stroboscope.

Single point source

1. Screw the bent metal rod onto the front of the place of the wave generator so that the rod points

forwards. Switch on the power and let the motor run slowly observe and draw a fig.1.

2. Place small pieces of paper on the water and see if they move. Are the pieces of paper displaced at the

wave speed? If not explain your observations.

3. Switch off the power and remove the bent metal rod. Lower the plane generator to touch just touch the

water surface.

4. Place the plane reflector at a small distance in front of the generator.

5. Observe the reflected pulse and draw a fig.2. Where is the center from which the reflected pulse seems

to diverge? Compare your observations with the plane mirror image of a light source.

6. Repeat step (3) using the two reflectors with a gap of 1-2cm between them observe and draw a fig.3 .

Where is the source from which the transmitted pulse seems to diverge? Compare your observation with

Huygen’s principle.

7. Place the metal parabolic reflector (convex side) so that the point source is at its focus. Give a single

push to the generator to produce a wave pulse. Observe (and draw a fig.4 ) the reflected pulse and

compare with the effect of a parabolic mirror when a light source is placed at its focus.

8. Repeat 7 metal parabolic reflector (concave side) observe and draw a fig.5

Two Synchronous point sources

Attach the two bent metal rods to the plate of the wave generator. Start the vibrator. Observe and observe and

draw a fig.4 the curves where the two waves interfere so that the water is at rest. Vary the frequency of the


waves by increasing the speed of the vibrator and observe observe and draw a fig.6 then explain the effect on

the interference pattern.

A Plane Wave

1. Use the plate of the wave generator itself as a source of waves. Produce waves with a wavelength about

2.5cm or to do this move the plate to and fro by hand.

2. Place the long reflector diagonally in the tank and observe reflected waves. Compare your observation

with the law of reflection for light observe and draw a fig.7.

3. Replace the long reflector by the two shorter reflectors parallel to the wave fronts 5-6cm away from the

wave generator and as far as possible from each other. Generate waves by hand or with the motor (about

2cm)observe observe and draw a fig.8. Decrease the distance between the two reflectors until about

1cm. Observe the wave fronts observe and draw a fig.9 then compare this with Huygen’s principle.

4. Place the very short reflector between the two reflectors so that two open spaces of 1cm or less are left

between the reflectors. Observe (and draw a fig.10) the interferences pattern and compare with the

results of experiment W4.2 and the experiment of Young.

5. Now remove the reflectors and put the rectangular plane block in the ripple tank at about 5cm from the

plane wave generator. The length of the block should parallel to the wave fronts observe and observe

and draw a fig.11.

6. Repeat 5 above with the block length about 450 to the wave front observe and draw a fig.12

The Report

The report should include the observations with carefully drawn neat figures and explanation where applicable

as well as answers to every question.


REFRACTIVE INDEX- B9 LAWS OF REFRACTION Aim: 1. Determination of refractive index of glass and water by

plotting (graphical method) (glass)

apparent depth method (water)

A. PLOTTING (GRAPHICAL METHOD)

APPARATUS

ABCD is a rectangular glass block.P1, P2, P3 and P4 are pins on a drawing board and paper.

Method

1. Place a rectangular glass block on a paper on the drawing board.

2. Draw line P as shown in the figure.

3. Look in along the direction of P1 and P2 until the image of line P through the glass is in line with the pins.

4. Remove the pins and mark their positions on the paper.

5. Repeat the procedure for 5 more lines namely Q, R, S, T, and U. To get pins P3 and P4, P5 and P6, P7 and P8 P9 and P10 and P11 and

P12. Make sure you mark the positions of the pins precisely.

6. Draw the outline of the glass block on the drawing paper.

7. Remove the glass block and pins from the paper.

8. Draw the normals at points E and F and join E&F.

9. Measure the angles i and R with a protractor, and calculate the refractive index. Repeat this for 5 more times and plot a graph of

sin i/sine r and get the refractive index of glass. Also calculate for each set of data sin i/sin r and get their average value. Compare

this with the one obtained from plotting.

I Sin i r Sin r Sin i/sin r

P

E

B

C D

A

F

P1

P2

r

i

i


B. APPARENT DEPTH METHOD

Apparatus

Glass or Perspex block B, traveling microscope M, lycopodium powder L and beaker.

ethod

Place the beaker B on a sheet of paper P and arrange the travelling microscope so that the microscope M and the scale s are vertical . Put a pin on the bottom of the beaker. Focus the microscope M on the pin. Having achieved a sharp focus using the fine adjustment screw take the reading r3 (fig (c)). of the vertical scale of the microscope.

NOW almost fill the beaker B with water. Move the microscope down until the pin seen through the water is in sharp focus. Take the reading r2 fig (b)). of the vertical scale of the microscope.

Focus the microscope M on the upper surface of the water which is sprinkled using a little lycopodium powder L or chalk dust if necessary Having achieved a sharp focus using the fine adjustment screw take the reading r1 (fig (a)). Of the vertical scale of the microscope.

Repeat the procedure above for 5 more different depths of water and fill the table below.

Measurements

r1 (mm) r2 (mm) r3 (mm) (r1-r2)

(mm)

(r1-r3) (mm)

1.

2.

3.

4.

5.

6.

Draw a graph of (r1-r3) (mm) versus (r1-r2) (mm) and find n for water graphically.

Conclusion:The refractive index of water is: Apparent method:…………+ ….%.The refractive index of

glass is: Plotting method:…………+ ….%.

(fig

(a)).

fig

(b)).

r1 r2

r3

(fig (c)).


C18 Charging curves of a capacitor and oscilloscope

AIM:

1. To learn how to use the oscilloscope

2. To find out the values of capacitors given. 3. To find out of the formulas for capacitors in 1. Series 2. Parallel are collect 4. Explain how the current of capacitor voltage in a series C-R circuit which is connected to a D.C source varies with time. 5. Draw graph for variation of voltage with time for each of the component in C-R circuit when the capacitor is

Charging Discharging

6. Define the time constant of a C-R circuit 7. Determine the growth and decay of the component voltage on current in a series C-R circuit, seconds after the

commencing of Charging Discharging

THEORY:

heated filament cathode

Focussing anode

electron beam

accelerating X-plates Y-plates

anode

NB. Disposition of control varies depending on the make of oscilloscope.

Operation of oscilloscope

The oscilloscope can be used to give an image of a repetitive signal as a function of time. The signal as a

voltage, is applied to the Y-plates (vertical movement) and internally generated wave sweeps the electron beam

(seen as a spot on the screen) horizontally at some pre-determined rate. This rate is set using the “time/division”

control.

The “time/division” control is calibrated such that when it is operating at 50 cps, 1 cycle occupies 20 ms. All the

other ranges on the switch are direct multiples of this. The time calibration is only valid at the minimum setting

of the “X-pos” control. The X-shift control moves the whole trace horizontally

The trace may also be controlled vertically using the “volt/div” control. This switch inserts a series of

resistances between the input socket and the vertical amplifier. It is used either to obtain a picture of convenient

height or to obtain direct readings of the input voltage (provided the “Y-pos” control is at its minimum setting).

To take measurements, a steady trace is required, and the “trig-level” control may be adjusted. You will be

using the internal trigger where the applied, i.e. unknown, signal is used to start the time base. The “trig-level”

switch controls the signal level at which the time base is triggered.

Reorganized by mr itune jk 0724682620 gk phy The “d.c. /a.c.” switch is normally set to the a.c. position. This inserts a block capacitor in series with the input of the

vertical amplifier to remove the d.c. Component of the signal.

Method A

1. Connect the signal generator up to the oscilloscope. Set the generator to output sine waves at a frequency of

500 Hz

2. You should see a steady sine wave on the screen. If not, press in the trigger level button. Adjust the intensity

and focus controls to give a sharp, but not too bright image.

3. Now try the effect of the following controls: X pos Y pos time/div volts/div

4. Measure the wavelength of the wave seen on the screen and calculate the frequency of the wave.

5. The oscilloscope can also be used to measure voltage, the voltage output of generator to 2.

6. Measure the voltage from the oscilloscope screen.

7. Now set the generator to give out square waves at 500 Hz and voltage output setting 2.

8. Measure the frequency and voltage of the wave.

9. Record all data on the worksheet. Comment and compare your results from the sine and square waves.

Method B:

1. When a capacitor is charging through a Resistor R1 ; The rate of charge of I or voltage VC at a particular instant depends on the value of I or voltage VC at that instant. Follows an exponential curve and the mathematical equation is

VC = E (1-e-t/CR1) and I = (E/R1)e-t/CR

1

2. When the capacitor is discharging the current I flows opposite to the charging

Current I through R2. VC starts to decay. The curve is an exponential as above

VC = Ee-t/CR2

And I =-(E/R2) e-t/CR2

3. The rate of charging or discharge at any particular time is shown by gradient or Slope of VC /time graph at that time. A

tangent drawn on the graph at any

Point indicates the slope and thus the rate of charge or discharge. If the rate of

VC

Discharge I

E/R2 t1

Charge

E/R1

Reorganized by mr itune jk 0724682620 gk phy Charge /discharge were not to charge but remain constant then the capacitor

Were to charge/discharge in a time = CR in seconds. This is called time constant T.

T = CR

APPARATUS:

1. Power supply 2. High resistance values R1 3. 5 unknown capacitors C1, C2, C3, C4, and C5 4. Discharging resistors RO

PROCEDURE I

Using the lowest value of C1; connect the circuit as shown in the above figure

Use the oscilloscope to determine the P.d across the capacitor as it charge through R1 with time.

Table this in a suitable table C1.

Make the capacitor to discharge through R2 and record the P.d across it with time.

Table this in table C1.

Repeat this for other values of capacitor C2, C3, and each time record P.d across the capacitor with time in a suitable table.

Draw on the same axis the graphs of P.d across capacitor against time (charging and discharging) for all the capacitors.

Worksheets

Sine wave

Generator

Frequency (Hz)

Length on

Screen (cm)

Time / div

(secs)

Time (secs) Oscilloscope

Frequency (Hz)

TP1

+ E10V

S2

R11M

R2100

C110uF


500

Voltage setting Height on screen (cm) Volt / div (volts) Voltage (volts)

2

Table C1 E = ______________ R1 = ___________ R2 = _________________

Time

Charging V (volts)

DischargingV (volts)

Table C2 E = ______________ R1 = ___________ R2 = _________________

Time

Charging V (volts)


Table C3 E = ______________ R1 = ___________ R2 = _________________

Time

Charging V (volts)

Discharging V (volts)

Table C1 and C2 series E = ______________ R1 = ___________ R2 = _________________

Time

Charging V (volts)


Table C1 and C3 series E = ______________ R1 = ___________ R2 = _________________

Time

Charging V (volts)


Reorganized by mr itune jk 0724682620 gk phy Table C2 and C3 series E = ______________ R1 = ___________ R2 = _________________

Time

Charging V (volts)


Table C1 ,C2 and C3 series E = ______________ R1 = ___________ R2 = _________________

Time

Charging V (volts)

Discharging V (volts)

Table C1 and C2 parallel E = ______________ R1 = ___________ R2 = _________________

Time

Charging V (volts)



Time

Charging V (volts)



Time

Charging V (volts)


Table C1 ,C2 and C3 parallel E = ______________ R1 = ___________ R2 = _________________

Time

Reorganized by mr itune jk 0724682620 gk phy Charging V (volts)


Work to do:

1. Determine the value of the capacitors from the graph

C1 = C2 = C3 = C1 and C2 series C1 and C3 series C2 and C3 series C1 and C2 parallel C1 and C3 parallel C2 and C3 parallel C1 ,C2 and C3 series C1 ,C2 and C3 parallel

2. What can you deduce from the graphs?

Questions:

1. A 0.5µF capacitor is connected to a 200V supply via a supply a 150 capacitor. Ignoring lead resistance, calculate the circuit time constant and the capacitor and the capacitor voltage after a time equal to the time constant.

2. A 10µF capacitor is fully charged via a total resistance of 22KV to 250V. Calculate the capacitance voltage 10ms after charging commenced. How long did it take for the capacitor to be fully

charged.

3. Determine the value of time constant when charging for each capacitor.

4. A capacitor is fully charged to a p.d of 200V. when discharged through a 250 resistor the capacitor voltage falls to 45V in 0.3s. calculate the Capacitance of a capacitor and the time constant.


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C20 ~ Kirchhoff's Laws