Basic Electrical Circuirt lab

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University of KwaZulu-Natal

SCHOOL OF

ELECTRICAL, ELECTRONIC & COMPUTER ENGINEERING

Practical No : EL2EL1

Course : ELECTRICAL ENGINEERING

Codes : ENEL2ELH1

Title : TRANSIENTS IN RC CIRCUITS

1. Introduction

Networks containing resistors and capacitors find wide application in many branches of electrical

engineering. The purpose of this practical is to investigate the charging and discharging

characteristics of some simple circuits of this type.

2. Theory

2.1 RC charging characteristics

2 R

Ohms

t = 0

1 i

Vo amps C vC

volts Farads volts

0 V

Figure 1. RC circuit.

Consider the circuit shown in Figure 1. Capacitor C is connected via a resistor R and a switch, either

to a DC voltage Vo or to 0 V. If the switch is in position 1 for some time, the capacitor C will be

discharged and VC = 0 V. If the switch is moved to position 2 at a time t = 0, then a little mathematics

will show that the voltage across the capacitor vC and the current into the circuit, as a function of time

t, are given by:

)1(eR

Viand)e(1Vv /t-O/t-OC

where = RC seconds is the time constant of the circuit.

2.2 RC discharging characteristics 2 R

Ohms

t = 0

1 i

Vo amps C vC

volts Farads volts

0 V

Figure 2. RC circuit.

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If, after the capacitor has been charged to the point where vC = VO volts the switch is changed from

position 2 to position 1 at time t = 0, then some more mathematics will show that the voltage across

the capacitor vC and the current i through the resistor are given by the expressions:

)2(eR

ViandeVv /t-O/t-OC

where = RC seconds, the time constant of the circuit. See Figure 2. Note that the direction of

current i is now reversed as the capacitor has become the voltage source.

The charging and discharging characteristics are given in Figure 3 for Vo = 5 volts and = 5 time

constants. The voltage across the capacitor vC, after a period of one time constant, is given for both

the charging curve and discharging curve.

Figure 3. RC charging and discharging waveforms

2.3 Connecting two capacitors

t = 0 R

Ohms

i

V1 C1 amps C V2 volts Farads Farads volts

0 V

Figure 4. RC circuit with two capacitors.

If the voltage across C1 is V1 and the voltage across C is V2 before closing the switch, then after

closing the switch still more mathematics will show that the voltage across both capacitors eventually

becomes equal to V where:

3

. )a3(CC

CVVCV

1

211

The current i during the time the capacitor voltages are changing is given by the expression:

)b3(eR

VVi /t-21

where the time constant is now given by the expression:

)c3(CC

CCR

1

1

Note that the term CC

CC

1

1 is the capacitance of C1 and C in series.

Figure 5. RC charging and discharging waveforms for two capacitors with parameters as indicated.

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3. Experimental Procedure

To confirm the theoretical predictions in the previous section, the charging and discharging voltage

waveforms of a capacitor in an RC circuit are measured and plotted using a custom-built electronic

stopwatch. A time constant of 1 second has been selected with resistor R = 1 M and C = 1 F so

that the charging and discharging characteristics can be observed on an oscilloscope. In practice, the

time constants of RC circuits vary from nanoseconds to seconds to perform such functions as

differentiation, integration and timing. The voltages are measured using the electronic stopwatch

shown in Figure 6 which makes use of the accuracy of a Digital Multimeter (DMM).

Figure 6. Block diagram of the RC measuring system. Note that initially capacitor C1 is not used.

Figure 7. The output voltage waveform at BNC terminal VC2 or PCB test point TP4.

The exponential waveform at VC2 stops rising when the voltage VC reaches VM volts, a voltage set by

the user. The time taken to reach this voltage appears as a steady dc voltage VC2 at the output. It is

numerically equal to time tM and can be measured accurately with a DMM.

+5 V

TP6

S1

VS1

0 V

S2

C1

R

1 M

C 1 F

2.2 F

S3

VC1

VC

Start at t = 0

Stop at VM

TP2

RV1

10 k

+5 V

VM

VM

TP3

Reset

Reset

Electronic stopwatch

Readout t = 0

TP4

VC2 = k tM where

k = 1 Vs-1

VC2

0V RC Network Set VM Output to DMM

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RV1 S1 S2 S3 S4 Vc Vc2 I Control

Closed Vs1 Vc1 Norm

Open 0 V Vc Reset

0 V 5 V TP2 TP4 TP5

Figure 8. The control panel.

C R +5 V C1

TP6

Terminals

0 V Rail

GND

VC VC VC2 VM

TP1 TP2 TP4 TP3

Figure 9. The printed circuit board.

All your results and conclusions must be recorded on pages 9 and 10.

3.1 Charging characteristic

Very accurate results may be achieved in this practical as the electronic stopwatch can measure time

with an accuracy of about 10 ms. The resistors and capacitors have tolerances of 5%, so if the

nominal resistor and capacitor values are used then = RC = 1 0.1 s. The actual RC time constant

will now be determined.

(a) Measure the values of R (1 M ) and C (1 uF) using the DMM and calculate your particular RC time constant for the components supplied for this practical. Record the results in Table 6

on page 9.

(b) Insert the 1 F capacitor into the terminals marked C and the 1 M resistor into the terminals marked R by pressing down on the terminals on the printed circuit board (PCB). See Figure 9.

Switch on the trainer breadboard.

(c) A +5 V regulated dc supply is used on the PCB. Measure this dc voltage (to 2 decimal places) at TP6 on the PCB using the DMM with the negative (black) lead connected to the 0 V rail

test point. See Figure 9. Record the result in Table 7 on page 9.

(d) Put switches S1, S2 and S3 into the following positions, S1 (closed), S2 (VS1 position) and S3 (VC position). Refer to the diagram of the control panel in Figure 8. The +5 V supply

charges capacitor C via switch S1, switch S2 and resistor R. Refer to the circuit diagram in

Figure 6. The voltage across capacitor C is connected to the stop input of the electronic

stopwatch by switch S3. After several seconds the voltage VC across the capacitor will reach

+5 V. Measure and record in Table 8 on page 9 the final voltage VC at TP2 on the circuit

board using the DMM.

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3.2 Using an oscilloscope to observe the charging and discharging waveforms of capacitor C

(a) Connect the VC BNC output (same as TP2) to CH1 of the oscilloscope using a BNC to BNC lead. Set the switch settings on the oscilloscope as indicated in Table 1.

Table 1. Initial switch settings for the oscilloscope.

TIME/DIV 0.5 s

TRIG AUTO

MODE CH1

VOLTS/DIV 1

VAR CAL

AC/DC DC

GND IN

(b) Adjust the vertical position control so that the trace is at the bottom of the graticule. This line now represents 0 V. Also, adjust the horizontal position control so that the trace

starts at the extreme left-hand side of the graticule. Release the GND button. The trace

should now move from move up 5 divisions. This line represents +5 V, as the capacitor

will be fully charged.

(c) Discharge capacitor C by moving switch S2 to the 0 V position. Voltage VC will gradually decay to zero producing a decay curve as shown in Figure 3.

(d) Charge capacitor C by moving switch S2 to the VS1 position. Capacitor C will gradually charge up to +5 V producing a charging curve as shown in Figure 3.

(e) Sketch the observed waveforms on page 9 under Section 3.2.

Note that the persistence of the oscilloscope screen is insufficient to form continuous lines as shown

in Figure 3, which makes it difficult to verify that the charging and discharging characteristics are

exponential in nature. Also, note that the oscilloscope is not synchronised to switch S2 and so that the

curves do not start at the left-hand side of the graticule.

3.3 Measuring and plotting the charging waveform

In this section, the charging waveform illustrated in Figure 3 will be confirmed. As explained in

Section 3, a DMM is able to measure steady voltages very accurately but is unable to measure

voltages such as VC that are changing. This problem is overcome in this practical using the electronic

stopwatch which determines the time tM that elapses between the switch S2 closing at t = 0 and the

time when voltage VC reaches a specific set voltage VM.

Charging measurement procedure

First, set VM at TP3 using potentiometer RV1 to a suitable value using the DMM (e.g. +1.00 V).

Then put the switches into the positions given in Table 2 in the order given. Now measure VC2 at TP4

on the PCB. This voltage is equal to time tM. Record VM and tM in Table 9 on page 9.

Reset VM to a new value and re-measure tM. Plot VM as a function of tM while the measurements are

in progress. About ten different values of VM, suitably spaced, will give an accurate curve.

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Table 2. Switch settings for measuring voltage VC while charging

Switch Position Action

S1 Closed

S2 0 V Discharges C

Wait 5 seconds for C to discharge

S3 VC

S4 Press Reset Discharges C2

S2 VS1 Charges C

3.4 Measuring and plotting the discharging waveform

The discharging characteristic can be measured and plotted in the same way by moving switch S2

from the VS1 position to the 0 V position. See Figure 6.

Discharging measurement procedure

First, set VM at TP3 using RV1 to a suitable value (e.g. +4.00 V). Then put the switches into the

positions given in Table 3. Now measureVC2 at TP4 on the PCB. This voltage is equal to time tM.

Record VM and tM in Table 10 on page 9.

Reset VM to a new value and re-measure tM. Plot VM as a function of tM while the measurements are

in progress. About ten different values of VM, suitably spaced, will give an accurate curve.

Table 3. Switch settings for measuring voltage VC while discharging.


S1 Closed

S2 VS1 Charges C

S3 VC


S2 0V Discharges C

3.5 Connecting two capacitors

In this section an additional capacitor C1 will be charged to +5 V and then connected to capacitor C

via resistor R. The charging of C and discharging of C1 will be measured and plotted. Refer to

Section 2.3 and Figure 6.

(a) Measure the value of C1 (2.2 uF) using the DMM. Calculate your particular final voltage V using Equation (3a) and new time constant using Equation (3c) for the components

supplied for this practical. Record the results in Table 11 on page 10.

(b) Insert the 2.2 F capacitor into the terminals marked C1 on the PCB. See Figure 9.

(c) Measure the final voltage across capacitor C at TP2 using the DMM. This is done by closing switch S1 to charge C1 up to +5 V. See Figure 6. Now discharge C by setting

switch S2 in the 0 V position. Switch S3 should be in the VC position and the DMM

should read 0 V as C is discharged. Now open S1 to disconnect the +5 V supply. Finally,

move switch S2 to the VS1 position. Capacitors C1 and are now connected via resistor R

with C1 charging C. The reading on the DMM will rise over a period of time to the final

voltage V. Record this voltage in Table 12 on page 10.

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Measurement procedure charging of capacitor C

Measure and plot the charging characteristic of C by adjusting VM at TP3 to suitable values, e.g.

0.50V, but < V in Equation (3a). Set the switches as given in Table 4 below. Now measure VC2 at

TP4 on the PCB. This voltage is equal to time tM. Record VM and tM. in Table 13 on page 10.

Reset VM to a new value and re-measure tM following the procedure given above. Plot the charging

characteristic of C by plotting VM as a function of tM. Compare your curve with that in Figure 5.

Table 4. Switch settings for measuring voltage VC while C1 charges C.


S1 Closed Charges C1 to +5V

S2 0V Discharges C


S3 VC To sense VC S4 Press Reset Discharges C2

S1 Open Disconnects +5V

S2 VS1 C1 charges C

Measurement procedure discharging of capacitor C1

Measure and plot the discharging characteristic of C1 by adjusting VM at TP3 to suitable values, e.g.

4.75 V, but >V in Equation 3(a). Set the switches as given in Table 5 below. Now measureVC2 at TP4

on the PCB. This voltage is equal to time tM. Record VM and tM in Table 14 on page 10.

Reset VM to a new value and re-measure tM following the procedure given above. Plot the discharging

characteristic of C1. Compare your curve with that in Figure 5.

Table 5. Switch settings for measuring voltage VC1 while C1 charges C.


S1 Closed Charges C1

S2 0 V Discharges C


S3 VC1 To sense VC2


S1 Open Disconnects +5 V

S2 VS1 C1 charges C

4. Pre-practical Requirements

It is essential to prepare for this laboratory practical by reading and understanding the procedures.

Derive the three sets of equations making use of Kirchhoff's laws.

5. Laboratory Report

If you are required to produce a full report on this practical, then it is recommended that you plot the

theoretical and measured curves using Matlab to determine the accuracy of your measurements.

Reference

Edminster, Electric Circuits, McGraw-Hill (Schaum Outline Series), 3rd

Edition, 1997

A D Broadhurst & G W Vth 5 December 2005

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RESULTS: ET1 TRANSIENTS IN RC CIRCUITS PRACTICAL

Section 3.1 Charging characteristic (a) Table 6. Measured values of R

and C

R

C

= RC

(c) Table 7. Measured value of the

supply voltage

Vo

(e) Table 8. Measured final

voltage VC VC

Sections 3.2 Using an oscilloscope to observe the charging and discharging waveforms of C

Sections 3.3 and 3.4 Measuring and plotting the charging waveform

Table 9. Measured values of VM and tM while

charging C

VM

(V)

tM

(s)

0.00 0.00

Table 10. Measured values of VM and tM while

discharging C

VM

(V)

tM

(s)

Vo = 0.00

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Section 3.5 Connecting two capacitors

(a) Table 11. Measured values and calculated parameters

C1

C

C//C1

R

V0

V

Eqn. (3a)

= R x C//C1

Eqn. (3c)

(c) Table 12. Measured final voltage V V

Table 13. Measured values of VM and tM for

C charging

VM

(V)

tM

(s)

0.00 0.00

Table 14. Measured values of VM and tM for C1

discharging

VM

(V)

tM

(s)

V0 = 0.00

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UNIVERSITY OF KWAZULU-NATAL

SCHOOL OF

ELECTRICAL, ELECTRONIC & COMPUTER ENGINEERING

PRACTICAL NO : EL2EL1

COURSE : ELECTRICAL ENGINEERING

CODE : ENEL2ELH1

TITLE : TRANSIENTS IN RC CIRCUITS

EQUIPMENT LIST

1 x ISO-Tech digital multimeter + test leads

1 x ISO-Tech dual trace oscilloscope

2 x BNC to BNC cables

1 x Trainer

1 x PC plug-in trainer board for ET1 Prac "Transients in RC Circuits"

1 x 1 F capacitors

1 x 2.2 F capacitors

1 x 1M resistor 5%

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Basic Electrical Circuirt lab