some practical laboratory experiments

Laboratory Experiments

Some practical laboratoryexperiments

Ten straightforward practical laboratory experiments are included to help supplement and enhance academicstudies.These exercises may be edited by tutors to suit availability of equipment and components.The list of experiments is not exhaustive, but covers some of the more important aspects of early electricalengineering studies.

Experiments covered are:

1. Ohm’s law (see Chapter 2)

2. Series-parallel d.c. circuit (see Chapter 5)

3. Superposition theorem (see Chapter 13)

4. Thévenin’s theorem (see Chapter 13)

5. Use of CRO to measure voltage, frequency and phase (see Chapter 14)

6. Use of CRO with a bridge rectifier circuit (see Chapter 14)

7. Measurement of the inductance of a coil (see Chapter 15)

8. Series a.c. circuit and resonance (see Chapter 15)

9. Parallel a.c. circuit and resonance (see Chapter 16)

10. Charging and discharging a capacitor (see Chapter 18)

Copyright © 2010 John Bird. Published by Elsevier Ltd. All rights reserved.DOI: 10.1016/B978-1-85617-770-2.00046-X

Copyright © 2010 John Bird. Published by Elsevier Ltd. All rights reserved.

2 Electrical Circuit Theory and Technology

1 Ohm’s Law

Objectives:

1. To determine the voltage-current relationship in ad.c. circuit and relate it to Ohm’s law.

Equipment required:

1. D.C. Power Supply Unit (PSU).

2. Constructor board (for example, ‘Feedback’EEC470).

3. An ammeter and voltmeter or two Flukes (forexample, 89).

4. LCR Data bridge.

Procedure:

1. Construct the circuit shown below with R = 470 �.

D.C.PSU

AI

RV

2. Check the colour coding of the resistor and thenmeasure its value accurately using an LCR databridge or a Fluke.

3. Initially set the d.c. power supply unit to 1V.

4. Measure the value of the current in the circuit andrecord the reading in the table below.

5. Increase the value of voltage in 1V increments,measuring the current for each value. Complete thetable of values below.

Resistance R = 470�

[colour code is:

……………………… ]

Voltage V (V) 1 2 3 4 5 6 7 8

Current I (mA)

6. Repeat procedures 1 to 5 for a resistance value ofR = 2.2 k� and complete the table below.

Resistance R = 2.2 k�

[colour code is:

………………………]

Voltage V (V) 1 2 3 4 5 6 7 8

Current I (mA)

7. Repeat procedures 1 to 5 for a resistance value ofR = 10 k� and complete the table below.

Resistance R = 10 k�

[colour code is:

……………………… ]

Voltage V (V) 1 2 3 4 5 6 7 8

Current I (mA)

8. Plot graphs of V (vertically) against I (horizon-tally) for R = 470�, R = 2.2 k� and R = 10 k�

respectively.

Conclusions:

1. What is the nature of the graphs plotted?

2. If the graphs plotted are straight lines, determinetheir gradients. Can you draw any conclusions fromthe gradient values?

3. State Ohm’s law. Has this experiment provedOhm’s law to be true?


Some practical laboratory experiments 3

2 Series–parallel d.c. circuit

Objectives:

1. To compare calculated with measured values ofvoltages and currents in a series–parallel d.c.circuit.

Equipment required:

1. D.C. Power Supply Unit (PSU).


3. An ammeter and voltmeter or a Fluke (forexample, 89)

4. LCR Data bridge.

Procedure:

1. Construct the circuit as shown below.

IT

I1

I2

20 V

R35 680 V R45 470 V

R55 390 V

R25 1kV

R15 330 V

1 2

2. State the colour code for each of the five resistorsin the above circuit and record them in the tablebelow.

3. Using a Fluke or LCR bridge, measure accuratelythe value of each resistor and note their values inthe table below.

Resistor R1 R2 R3 R4 R5

Colour code

Exact value

4. Calculate, using the exact values of resistors, thevoltage drops and currents and record them in thetable below.

Quantity Calculated value Measured value

VR1

VR2

VR3

VR4

VR5

IT

I1

I2

5. With an ammeter, a voltmeter or a Fluke, measurethe voltage drops and currents and record them inthe above table.

Conclusions:

1. Compare the calculated and measured values ofvoltages and currents and comment on any discrep-ancies.

2. Calculate the total circuit power and the powerdissipated in each resistor.

3. If the circuit was connected for 2 weeks, calculatethe energy used.



3 Superposition theorem

Objectives:

1. To measure and calculate the current in each branchof a series–parallel circuit.

2. To verify the superposition theorem.

Equipment required:


2. D.C. Power Supply Units.

3. Digital Multimeter, such as a Fluke (for exam-ple, 89).

4. LCR Data bridge.

Procedure:

1. Construct the circuit as shown below, measuringand noting in the table below the exact values ofthe resistors using a Fluke or LCR bridge.

IA

R1

R3

R2

IB

IC

12 V10 V

820 V680 V

1 kV

2. Measure the values of IA, IB and IC and record thevalues in the table below.

R1 (�) R2 (�) R3 (�)

IA (mA) IB (mA) IC (mA)

3. Remove the 12 V source from the above circuitand replace with a link, giving the circuit shownnext.

I1 I3

I2

10 V

820 V680 V

1 kV

4. Measure the values of I1, I2 and I3 and record thevalues in the table below.

Measured Measured MeasuredI1 (mA) I2 (mA) I3 (mA)

Calculated Calculated CalculatedI1 (mA) I2 (mA) I3 (mA)

5. Calculate the values of I1, I2 and I3 and record thevalues in the above table.

6. Replace the 12 V source in the original circuit andthen replace the 10 V source with a link, giving thecircuit shown below.

I6 I4

I5

12 V

820 V680 V

1 kV

7. Measure the values of I4, I5 and I6 and record thevalues in the table below.

Measured Measured MeasuredI4 (mA) I5 (mA) I6 (mA)

(Continued )



Calculated Calculated CalculatedI4 (mA) I5 (mA) I6 (mA)

8. Calculate the values of I4, I5 and I6 and record thevalues in the above table.

9. By superimposing the latter two diagrams on topof each other, calculate the algebraic sum of thecurrents in each branch and record them in the tablebelow.

Measured Measured MeasuredIA = I1 − I6 IB = I4 − I3 IC = I2 + I5

Calculated Calculated CalculatedIA = I1 − I6 IB = I4 − I3 IC = I2 + I5

Conclusions:

1. State in your own words the superposition theorem.

2. Compare the measured and calculated values ofIA, IB and IC in procedure 9 and comment on anydiscrepancies.

3. Compare these values of IA, IB and IC with thosemeasured in procedure 2 and comment on anydiscrepancies.

4. Can the principle of superposition be applied in acircuit having more than two sources?



4 Thévenin’s theorem

Objectives:

1. To calculate Thévenin’s equivalent of a givencircuit.

2. To verify Thévenin’s theorem.

Equipment required:


2. D.C. Power Supply Units.


4. LCR Data bridge.

Procedure:

1. Construct the circuit as shown below, measuringand noting in the table below the exact values ofthe resistors using a Fluke or LCR bridge.

IA

R1

R3

R2

IB

IC

12 V10 V

820 V680 V A

B

1 kV

2. Measure the values of IA, IB and IC and record thevalues in the table below.

R1 (�) R2 (�) R3 (�)

IA (mA) IB (mA) IC (mA)

3. Remove the 1 k� resistor from the above circuitand measure the open circuit voltage VOC at theterminals AB. Record the value in the table below.

4. With the 1 k� resistor still removed, remove thetwo voltage sources replacing each with a link.

Now measure the resistance rOC across the opencircuited terminals AB and record the value in thetable below.

Measured Measured Calculated CalculatedVOC (V) rOC (�) VOC (V) rOC (�)

5. Calculate values of VOC and rOC and record thevalues in the above table.

6. Compare the measured and calculated values ofVOC and rOC.

7. Using the calculated values of VOC and rOC cal-culate and record the current IC from the circuitbelow.

IC

Voc

roc

A

B

1 kV

IC (µA)

8. Compare this value of IC with that initially mea-sured in the original circuit (i.e. procedure 2).

9. Calculate the voltage V shown in the circuit below,using your calculated value of IC, and record thevalue in the table below.

IA IB

IC

12 V10 V

V V

820 V680 V A

B

1 kV



10. The terminal voltage of a source, V = E − I ×r.Using this, calculate and record the valuesof IA and IB, i.e. transpose the equations:V = 10 − IA × 680 and V = 12 − IB × 820.

V (V) IA (mA) IB (mA)

11. Compare these values of IA and IB with thoseinitially measured in the original circuit (i.e.procedure 2).

Conclusions:

1. State in your own words Thévenin’s theorem.

2. Compare the measured and calculated values of IA,IB and IC and comment on any discrepancies.

3. Can Thévenin’s theorem be applied in a circuithaving more than two sources?

4. If the 1 k� resistor is replaced with (a) 470�

(b) 2.2 k�, calculate the current flowing betweenthe terminals A and B.



5 Use of a CRO to measure voltage,frequency and phase

Objectives:

1. To measure a d.c. voltage using an oscilloscope.

2. To measure the peak-to-peak voltage of a waveformand then calculate its r.m.s. value.

3. To measure the periodic time of a waveform andthen calculate its frequency.

4. To measure the phase angle between two wave-forms.

Equipment required:

1. Cathode ray oscilloscope (for example, ‘Phillips’digital Fluke PM3082).


3. Function Generator (‘Escort’ EFG 3210).

4. D.C. Power Supply Unit.

5. Fluke (for example, 89).

Procedure:

1. Switch on the oscilloscope and place the trace atthe bottom of the screen.

2. Set the d.c. power supply unit to 20 V, making surethe output switch is in the off position.

3. Connect a test lead from channel 1 of the CRO tothe d.c. PSU.

4. Switch on the output of the d.c. PSU.

5. Measure the d.c. voltage output on the CRO.

d.c. voltage

6. Connect up the circuit as shown below.

Vs V1

V2

2.2 mF

100 V

7. Set the function generator to output a voltage of 5 Vat 500 Hz.

8. Measure the peak-to-peak voltages at V1 and V2using the CRO and record in the table below.

9. Calculate the r.m.s. values corresponding to V1 andV2 and record in the table below.

10. Measure the voltages V1 and V2 using a Fluke.

11. Measure the periodic time of the waveformsobtained at V1 and V2 and record in the table below.

12. Calculate the frequency of the two waveforms andrecord in the table below.

Voltage Peak-to-peak r.m.s. valuevoltage

V1

V2

Voltage Periodic time Frequency

V1

V2

13. Measure the phase angle φ between the two wave-forms using:

φ = displacement between waveforms

periodic time×360◦

= tT

× 360◦

(For example, if t = 0.6 ms and T = 4 ms, then

φ = 0.6

4× 360◦ = 54◦)

Volts

Input voltage (V1)

Time

Voltage across resistor (V2)

t

T

Phase angle

Conclusions:

1. Is a measurement of voltage or current with a Flukean r.m.s. value or a peak value?

2. Write expressions for the instantaneous val-ues of voltages V1 and V2 (i.e. in the formV = A sin(ωt ±φ) where φ is in radians).



6 Use of a CRO with a bridgerectifier circuit

Objectives:

1. To measure and observe the input and outputwaveforms of a bridge rectifier circuit using a CRO.

2. To investigate smoothing of the output waveform.

Equipment required:

1. Cathode Ray Oscilloscope (for example, ‘Phillips’digital Fluke PM3082).


3. Transformer (for example, IET 464).

4. Bridge rectifier.

5. Fluke (for example, 89).

Procedure:

1. Construct the circuit shown below with a mainstransformer stepping down to a voltage V1 between15 V and 20 V.

2. Measure the output voltage V1 of the transformerusing a Fluke and a CRO. Sketch the waveform.

3. Measure the output voltage V2 of the bridge rectifierusing a Fluke and observe the waveform using aCRO. Sketch the waveform.

4. Place a 100µF capacitor across the terminals ABand observe the waveform across these terminalsusing a CRO. Measure the voltage across terminalsAB, V3, sketch the waveform.

5. Place a second 100µF capacitor in parallel withthe first across the terminals AB. What is theeffect on the waveform? Measure the voltage acrossterminals AB, V4, sketch the waveform.

V1 r.m.s. V2 d.c. V3 d.c. V4 d.c.

Conclusions:

1. What is the effect of placing a capacitor across thefull-wave rectifier output?

2. What is the total capacitance of two 100µF capac-itors connected in parallel?

3. What is meant by ripple? Comment on the rip-ple when (a) one capacitor is connected, (b) bothcapacitors are connected.

V1 V2

A

RectifierTransformer

B

230 V 1 k�



7 Measurement of the inductanceof a coil

Objectives:

1. To measure the inductance of a coil.

Equipment required:


2. D.C. Power Supply Unit.

3. Function Generator (for example, ‘Escort’ EFG3210).

4. Unknown inductor.


6. LCR Data bridge.

Procedure:

1. Construct the circuit, with the inductance ofunknown value, as shown below.

Supply CoilV

A

B

A

2. Connect a d.c. power supply unit set at 1 V to theterminals AB.

3. Measure the voltage V and current I in the abovecircuit.

4. Calculate the resistance R of the coil, using

R = V

Irecording the value in the table below.

5. Connect an a.c. function generator set at 1V, 50 Hzto the terminals AB.

6. Measure the voltage V and current I in the abovecircuit.

7. Calculate the impedance Z of the coil, using

Z = V

I, recording the value in the table below.

8. From the impedance triangle, Z 2 = R2 + X 2L ,

from which, XL = √Z 2 − R2. Calculate XL and

record the value in the table below.

R(�) Z(�) XL = √(Z2 −R2)(�) L = XL

2πf(H)

9. Since XL = 2π fL then L = X L2π f ; calculate induc-

tance L and record the value in the table above.

10. Hence, for the coil, L = . . . H

and resistance, R = . . . �.

11. Measure the inductance of the coil using an LCRdata bridge.

12. Using an ammeter, a voltmeter or a Fluke, measurethe resistance of the coil.

Conclusions:

1. Compare the measured values of procedures 11 and12 with those stated in procedure 10 and commenton any discrepancies.



8 Series a.c. circuit and resonance

Objectives:

1. To measure and record current and voltages in ana.c. series circuit at varying frequencies.

2. To investigate the relationship between voltage andcurrent at resonance.

3. To investigate the value of current and impedanceat resonance.

4. To compare measured values with theoretical cal-culations.

Equipment required:

1. Cathode Ray Oscilloscope (for example, ‘Philips’digital Fluke PM3082).




5. LCR Data bridge.

Procedure:

1. Construct the series RCL circuit as shown below,measuring and noting the exact values of R, Cand L .

I

1 �F

CL

A.C. SupplyFunction

Generator

R

220 � 100 mH, 7 �

2. Set the a.c. supply (function generator) to 2 V at100 Hz.

3. Measure the magnitude of the current in the circuitusing an ammeter or Fluke and record it in the tablenext.

4. Measure the magnitudes of VR, VC and VL andrecord them in the table on the next column.

5. Calculate the values of XL and XC and record themin the table below.

6. Using the values of circuit resistance (which isR + resistance of coil), XL and XC, calculateimpedance Z .

7. Calculate current I using I = V

Z8. Repeat the procedures 2 to 7 using frequencies of

200 Hz up to 800 Hz and record the results in thetable below. Ensure that the voltage is kept constantat 2 V for each frequency.

Supply Measured Measured Measured MeasuredvoltageV I (mA) VR (V) VC (V) VL (V)

2 V, 100 Hz

2 V, 200 Hz

2 V, 300 Hz

2 V, 400 Hz

2 V, 500 Hz

2 V, 600 Hz

2 V, 700 Hz

2 V, 800 Hz

Supply Calculate Calculate Calculate Calculate

voltageV XL (�) XC (�) Z (�) I = VZ

(mA)

2 V, 100 Hz

2 V, 200 Hz

2 V, 300 Hz

2 V, 400 Hz

2 V, 500 Hz

2 V, 600 Hz

2 V, 700 Hz

2 V, 800 Hz

9. Plot a graph of measured current I (vertically)against frequency (horizontally).

10. Plot on the same axes a graph of impedance Z(vertically) against frequency (horizontally).



11. Determine from the graphs the resonant freq-uency, fr .

12. State the formula for the resonant frequency of aseries LCR circuit. Use this formula to calculatethe resonant frequency fr .

13. Set the supply voltage to 2 V at the resonant fre-quency and measure the current I and voltages VR,VC and VL.

14. Connect a cathode ray oscilloscope such that chan-nel 1 is across the whole circuit and channel 2 isacross the inductor.

15. Adjust the oscilloscope to obtain both waveforms.

16. Adjust the function generator from 2 V, 100 Hz upto 2 V, 800 Hz. Check at what frequency the volt-age across L (i.e. channel 2) is a maximum. Noteany change of phase either side of this frequency.

Conclusions:

1. Compare measured values of current with the the-oretical calculated values and comment on anydiscrepancies.

2. Comment on the values of current I and impedanceZ at resonance.

3. Comment on the values of VR, VC and VL atresonance.

4. What is the phase angle between the supply currentand voltage at resonance?

5. Sketch the phasor diagrams for frequencies of(a) 300 Hz (b) fr (c) 700 Hz.

6. Define resonance.

7. Calculate the values of Q-factor and bandwidth forthe above circuit.



9 Parallel a.c. circuit and resonance

Objectives:

1. To measure and record currents in an a.c. parallelcircuit at varying frequencies.

2. To investigate the relationship between voltage andcurrent at resonance.

3. To calculate the circuit impedance over a range offrequencies.

4. To investigate the value of current and impedanceat resonance and plot their graphs over a range offrequencies.

5. To compare measured values with theoretical cal-culations.

Equipment required:




4. LCR Data bridge.

Procedure:

1. Construct the parallel LR – C circuit as shownbelow, measuring and noting the exact values ofR, C and L .

C 5 2.2 mF

IC

IS

ILR

A.C. SupplyFunction

Generator

L 5 100 mH,7 V

R 5 100 V

2. Set the function generator to 3 V, 100 Hz using aFluke.

3. Measure the magnitude of the supply current,IS, capacitor current, IC, and inductor branchcurrent ILR, and record the results in the tablenext.

4. Adjust the function generator to the other frequen-cies listed in the table ensuring that the voltageremains at 3 V. Record the values of the three cur-rents for each value of frequency in the table below.

Supply Measured Measured Measured Calculate

Voltage V IS (mA) IC (mA) ILR (mA) IC = V−JXC

3 V, 100 Hz

3 V, 150 Hz

3 V, 200 Hz

3 V, 220 Hz

3 V, 240 Hz

3 V, 260 Hz

3 V, 280 Hz

3 V, 300 Hz

3 V, 320 Hz

3 V, 340 Hz

3 V, 360 Hz

3 V, 380 Hz

3 V, 400 Hz

3 V, 450 Hz

Supply Calculate Calculate Calculate

Voltage V ILR = VR+JXLR

IS = IC+ ILR Z = VIS

3 V, 100 Hz

3 V, 150 Hz

3 V, 200 Hz

3 V, 220 Hz

3 V, 240 Hz

3 V, 280 Hz

3 V, 300 Hz

3 V, 320 Hz

3 V, 340 Hz

3 V, 360 Hz

3 V, 380 Hz

3 V, 400 Hz

3 V, 450 Hz



5. Calculate the magnitude and phase of IC, ILR andIS(= IC + ILR) for each frequency and record thevalues in the table on the previous page.

6. Calculate the magnitude and phase of the circuitimpedance for each frequency and record thevalues in the table on the previous page.

7. Plot a graph of the magnitudes of IS, IC, ILR andZ (vertically) against frequency (horizontally), allon the same axes.

8. Determine from the graphs the resonant frequency.

9. State the formula and calculate the resonantfrequency for the LR–C parallel circuit.

Conclusions:

1. Compare measured values of the supply current ISwith the theoretical calculated values and commenton any discrepancies.

2. Comment on the values of current I and impedanceZ at resonance.

3. Compare the value of resonance obtained fromthe graphs to that calculated and comment on anydiscrepancy.

4. Compare the graphs of supply current andimpedance against frequency with those for seriesresonance.

5. Calculate the value of dynamic resistance, RD andcompare with the value obtained from the graph.

6. What is the phase angle between the supply currentand voltage at resonance?

7. Sketch the phasor diagrams for frequencies of(a) 200 Hz (b) fr (c) 400 Hz.

8. Define resonance.

9. Calculate the values of Q-factor and bandwidth forthe above circuit.



10 Charging and discharging acapacitor

Objectives:

1. To charge a capacitor and measure at intervals thecurrent through and voltage across it.

2. To discharge a capacitor and measure at intervalsthe current through and voltage across it.

3. To plot graphs of voltage against time for bothcharging and discharging cycles.

4. To plot graphs of current against time for bothcharging and discharging cycles.

Equipment required:


2. D.c. power supply unit.

3. Digital multimeter, such as a Fluke (for example,89).

4. LCR Data bridge.

5. Stop watch.

Procedure:

1. Construct the series CR circuit as shown below,measuring the exact values of C and R.

100 µF

A

DC PowerSupply Unit

100 k V

1

2

1

2 V

2. Set the d.c. power supply unit to 10 V, making surethe output switch is in the off position.

3. Charge the capacitor, measuring the capacitor volt-age (in volts) at 5 second intervals over a period of60 seconds. Record results in the table next.

4. Discharge the capacitor, measuring the capacitorvoltage at 5 second intervals over a period of 60seconds. Record results in the table on the nextcolumn.

Time (s) 0 5 10 15 20 25 30

Charge VC (V)

Discharge VC (V)

Time (s) 35 40 45 50 55 60

Charge VC (V)

Discharge VC (V)

5. Again, charge the capacitor, this time measuringthe current (in µA) at 5 second intervals over aperiod of 60 seconds. Record results in the tablebelow.

6. Discharge the capacitor, measuring the current at5 second intervals over a period of 60 seconds.Record results in the table below.

Time (s) 0 5 10 15 20 25 30

Current IC (µA)

Discharge IC (µA)

Time (s) 35 40 45 50 55 60

Current IC (µA)

Discharge IC (µA)

7. Plot graphs of VC against time for both charge anddischarge cycles.

8. Plot graphs of IC against time for both charge anddischarge cycles.

9. Calculate the time constant of the circuit (usingthe measured values of C and R).

10. Take a sample of the times and calculate valuesof VC and IC using the appropriate exponentialformulae VC = V (1 − e−t /CR ), VC = Ve−t /CR andIC = Ie−t /CR .

Conclusions:

1. Compare theoretical and measured values of volt-ages and currents for the capacitor charging anddischarging.

2. Discuss the charging and discharging characteris-tics of the capacitor.

3. Comment on reasons for any errors encountered.

4. What is the circuit time constant? What does thismean? Approximately, how long does the voltageand current take to reach their final values?


some practical laboratory experiments

Documents

lcr data bridge

power supply unit

power supply units

cathode ray oscilloscope

bridge rectier circuit

supply function generator

theoretical calculated values

lcr bridge