TRANSIENT RESPONSE of AN RC CIRCUIT LAB REPORT

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 kΩ, 100 kΩ. o Digital Multimeter (DMM) o Electrolytic Capacitor 470 µF

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

Figure 4-1

Figure 4-2 1. Time constant τ = RC for a series RC circuit having C = 470 µF for R = 68 kΩ and R = 100 kΩ is calculated to gain a perspective of how the transient will take. A capacitor will be mostly charged or discharged after five time constant, 5τ. 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 kΩ. 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 kΩ and two C = 470 µF. The capacitors are put in parallel to each others. 2. The total capacitance for parallel capacitor (CT = C1 + C2) and the transient period 5τ 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 kΩ and two C = 470 µF. So, the capacitors are in series. 2.

The total capacitance for series capacitor (1/ CT = 1/ C1 + 1/ C2) and the transient period 5τ 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 constant

R = 68 kΩ

C = 468 µF

τ = 31.82 s

R = 100 kΩ

C = 468 µF

τ = 46.8 s

Table 4-1

Vc R = 68 kΩ

Time Intervals (s)

Vc R = 100 kΩ

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

11.84

0.173

11.60

0.434

11.87

0.132

11.67

0.327

220 240

Table 4-2

Charge graph

12V

8V

4V

0V 0s

40s

80s

120s

160s

200s

240s

280s

320s

200s

240s

280s

320s

V(C1:2) Time

Discharge graph 15V

10V

5V

0V 0s

40s V(U1:2,R3:2)

80s

120s

160s Time

Calculation:

1) Single Capacitor: R = 68 kΩ

C = 477.8 µF

τ =RXC

Transient period = 5τ

= 68 kΩ X 477.8 µF

= 5 X 32.49

= 32.49 s

= 162.45 s

R = 100 kΩ

C = 477.8 µF

τ =RXC

Transient period = 5τ

= 100 kΩ X 477.8 µF

= 5 X 47.78

= 47.78 s

= 238.9 s

2) Parallel Capacitor: C1 = 477.8 µF C2 = 472.7 µF CT = C1 + C2 CT = 477.8 µF + 472.7 µF CT = 0.0009505 F τ =RXC

Transient period = 5τ

= 100 kΩ X 950.5 µF

= 5 X 95.05

= 95.05 s

= 475.25 s

3) Series Capacitor: C1 = 477.8 µF C2 = 472.7 µF 1/ CT = 1/ C1 + 1/ C2 1/ CT = 1/470 µF + 1/470 µF CT = 0.0002376 F τ =RXC

Transient period = 5τ

= 100 kΩ X 237.6 µF

= 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, 5τ (τ = 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, 5τ (τ = 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.