EXPERIMENT NO: 4 TRANSIENT RESPONSE of AN RC CIRCUIT

EXPERIMENT 4: TRANSIENT RESPONSE OF AN RC CIRCUIT

Aims:

To study the transient response in storing an electrical charge on a capacitor in an

RC circuit.

To study the transient decay of an initial charge on a capacitor through a resistor.

To determine the time constant in an RC circuit and how it can be changed.

Apparatus:

o VDC = 12 V

o Breadboard

o Resistor: 68 k, 100 k.

o Digital Multimeter (DMM)

o Electrolytic Capacitor 470 F

Method:

(a) Transient Response of RC circuit when capacitor is single

Figure 4-1

Figure 4-2

1. Time constant = RC for a series RC circuit having C = 470 F for R = 68 k

and R = 100 k is calculated to gain a perspective of how the transient will take.

A capacitor will be mostly charged or discharged after five time constant, 5. This

also called as transient period which then recorded in Table 4-1.

2. The circuit of Figure 4-2 is constructed using the values of R and C given in step

1. A jumper wire is used for the switch to connect the resistor either to the voltage

source or to the reference node (ground). The negative side of the electrolytic is

checked to ensure that it is connect to the ground.

3. The VS is set to 12 volts. The jumper wire is left in the discharge position until the

voltage across the capacitor stabilizes at 0 volt.

4. Then the jumper wire is put in the charge position.

5. VC is recorded for every 20 seconds up to 4 minutes (240 seconds). Then, the

switch is left in up position until the voltage VC stabilizes at the maximum value

(when the second digit of the multimeter is no longer changing over 30 second

period) and that value is recorded in Table 4-2.

6. One person is assigned to call off time and the other person is assigned to read and

record down the voltage.

7. The jumper wire is put in the discharge position and the capacitor voltage VC is

recorded at the same time interval as in step 5.

8. Items 3 to 6 is repeated with R = 100 k. The values are recorded in Table 4-2.

(b) Transient Response of RC circuit when capacitors are in parallel

Capacitor in Parallel

1. RC circuit is constructed by using one R = 100 k and two C = 470 F. The

capacitors are put in parallel to each others.

2. The total capacitance for parallel capacitor (CT = C1 + C2) and the transient period

5 is calculated. The charging and discharging of the capacitor will be stabilized at

this period.

3. Step 3 and 4 in the first experiment is being repeated.

4. Step 5 is being repeated and that value is recorded in Table 4-3.

5. Step 6 and 7 is being repeated and that value is recorded in Table 4-3.

(b) Transient Response of RC circuit when capacitors are in series

Capacitor in Series

1.RC circuit is constructed by using one R = 100 k and two C = 470 F. So, the

capacitors are in series.

2. The total capacitance for series capacitor (1/ CT = 1/ C1 + 1/ C2) and the

transient period 5 is calculated. The charging and discharging of the capacitor

will be stabilized at this period.

3. Step 3 and 4 in the first experiment is being repeated.

4. Step 5 is being repeated and that value is recorded in Table 4-3.

5. Step 6 and 7 is being repeated and that value is recorded in Table 4-3.

Table of Results

Time constantR = 68 k C = 468 F = 31.82 s

R = 100 k C = 468 F = 46.8 s

Table 4-1

Time Intervals (s)

Vc R = 68 k

Vc R = 100 k

Charge Discharge Charge Discharge

0 0.00 11.91 0.00 11.84

20 4.87 7.36 3.628 8.69

40 7.76 4.67 6.10 6.27

60 9.44 3.024 7.84 4.60

80 10.41 2.011 8.02 3.394

100 10.99 1.325 9.86 2.494

120 11.34 0.866 10.44 1.852

140 11.55 0.596 10.86 1.371

160 11.68 0.406 11.14 1.025

180 11.76 0.276 11.35 0.764

200 11.81 0.190 11.49 0.578

22011.84 0.173 11.60 0.434

240 11.87 0.132 11.67 0.327

Table 4-2

Charge graph

Time

0s 40s 80s 120s 160s 200s 240s 280s 320sV(C1:2)

0V

4V

8V

12V

Discharge graph

Time

0s 40s 80s 120s 160s 200s 240s 280s 320sV(U1:2,R3:2)

0V

5V

10V

15V

Calculation:

1) Single Capacitor:

R = 68 k C = 477.8 F

= R X C Transient period = 5

= 68 k X 477.8 F = 5 X 32.49

= 32.49 s = 162.45 s

R = 100 k C = 477.8 F

= R X C Transient period = 5

= 100 k X 477.8 F = 5 X 47.78

= 47.78 s = 238.9 s

2) Parallel Capacitor:

C1 = 477.8 F C2 = 472.7 F

CT = C1 + C2

CT = 477.8 F + 472.7 F

CT = 0.0009505 F

= R X C Transient period = 5

= 100 k X 950.5 F = 5 X 95.05

= 95.05 s = 475.25 s

3) Series Capacitor:

C1 = 477.8 F C2 = 472.7 F

1/ CT = 1/ C1 + 1/ C2

1/ CT = 1/470 F + 1/470 F

CT = 0.0002376 F

= R X C Transient period = 5

= 100 k X 237.6 F = 5 X 23.76

= 23.76 s = 118.8 s

Discussion & Conclusion:

The function of a capacitor is to store an electrical charge and energy. The

voltage across the capacitor is related to the charge by the equation V = Q / C for

steady state values, or it can be expressed as an instantaneous value dv = dq / C

Capacitor also often used as a filter in the circuit.

When the time, t = 0, the voltage across the capacitor is zero because there

can’t be an instantaneous change in voltage across the capacitor. After five time

constant, 5 ( = RC), the capacitor will be mostly charge or discharge where it also

call as the transient period.

Based on the first test in this experiment, we discovered that the capacitor in

the circuit which has small value of resistor is charged and discharged faster than the

one with greater value of resistor. According to the formula of transient period, 5 (

= RC), the smaller the value of the resistor, the greater the transient period becomes

thus more time is needed for the capacitor to fully charged or discharged and vice

versa.

Then, in the second test of the experiment, the positions of the capacitors are

changed into parallel and series position. The capacitors in parallel are charged and

discharged slowly because the total value of the capacitor is increases (CT = C1 + C2).

While in the series position of the capacitors, the capacitors are charged and

discharged quickly because the total value of the capacitors is small

(1/ CT = 1/ C1 + 1/ C2).

We achieved our aim of this experiment since the charging curves and

discharging curves which are plotted on graph were theoretically similar. In addition,

we have learned and understood the factors that can affect the time for the capacitor to

be fully charged or discharged which are the resistors and the position of the

capacitors. Since the readings and values are taken manually, there are bound to be

errors in it. But, we still can conclude that our experiment is a success since our

percentage differences with the theoretical value is below 30% which is relevantly

small.