Capitol College

Spring Semester 2000

# Circuit Theory: EE - 159

Lab Experiment #5

## Capacitance and Transients

Andy Buettner

Instructor: Dr. Thomas

Due:

Section Page #

1. Title Page???????????? 1

1. Objective????????????. 3

1. Equipment Used?????????.. 3

1. Equipment used?????????.. 3

2. Materials used??????????. 3

1. Procedures???????????... 3

1. Part 1?????????????... 3

2. Part 2?????????????... 3

1. Results?????????????. 4

1. Table 1:????????????... 4

2. Diagram 1:???????????.. 4

3. Diagram 2:???????????.. 5

4. Table 2:????????????... 5

5. Table 3????????????.... 5

6. Table 4:????????????... 5

7. Table 5:?.???????????.. 6

8. Table 6:????????????... 6

9. Diagram 3:???????????.. 6

10. Diagram 4:???????????.. 7

1. Answers to Lab Questions?????. 7

1. Conclusions??????????... 9

1. Attachments??????????... 9

Objective

The objective of this lab is to use a specific circuit to study a simple resistor - capacitor combination to discover how capacitors charge and discharge. Then calculate the time constant to prove that the mathematical interpretation of the circuit is correct.

Equipment Used

1. ### Equipment used

1. DMM #31101515, 16018027

2. ET - 3100 Trainer #1514

3. EE - 159 Lab kit

1. Parts used

1. 56KW resistor

2. 100KW resistor

3. 220mF capacitor

Procedures

1. ### Part 1: Charging phase

1. Select a 56KW resistor and a 220mF capacitor.

2. Measure and record their actual values.

3. Construct the following circuit:

1. Power the Trainer to 5V.

2. Close the switch and record the voltage across the capacitor for two minutes at intervals of ten seconds.

3. Disconnect the circuit leaving the components fully charged..

1. Part 2: Discharging phase

1. Construct the following circuit:

1. Close the switch and measure the voltage across the capacitor for two minutes at intervals of ten seconds.

Repeat this procedure 2 additional times with the 56KW

resistor and 3 additional times with the 100KW resistor.

Results

Table 1: Resistor / Capacitor equivalent values

Indicated value

220 mF

#### 56KW

100KW

Actual value

222mF

54.6KW

97.7KW

Diagram 1: Schematic of Circuit 1 (Enlarged view)

Diagram 2: Schematic of circuit 2 (Enlarged view)

Table 2: Samples for the charging process using 56KW resistor

Time:

 Trial 0s 10s 20s 30s 40s 50s 60s 70s 80s 90s 100s 110s 120s 1 0v 2.40v 3.68v 4.18v 4.43v 4.58v 4.66v 4.71v 4.74v 4.77v 4.79v 4.81v 4.82v 2 0v 2.50v 3.79v 4.35v 4.61v 4.73v 4.80v 4.83v 4.85v 4.86v 4.86v 4.87v 4.87v 3 0v 2.45v 3.77v 4.33v 4.62v 4.76v 4.82v 4.85v 4.86v 4.87v 4.87v 4.87v 4.87v

Table 3: Samples for the discharging process using 56KW resistor

Time:

 Trial 0s 10s 20s 30s 40s 50s 60s 70s 80s 90s 100s 110s 120s 1 5.00v 2.53v 1.26v .62v .31v .15v .08v .04v .02v .01v .00v .00v .00v 2 5.00v 2.52v 1.26v .62v .30v .15v .07v .04v .02v .01v .00v .00v .00v 3 5.00v 2.51v 1.25v .59v .29v .14v .07v .04v .02v .01v .00v .00v .00v

Table 4: Samples for the charging process using 100KW resistor

Time:

 Trial 0s 10s 20s 30s 40s 50s 60s 70s 80s 90s 100s 110s 120s 1 0v 1.56v 2.69v 3.46v 3.93v 4.23v 4.45v 4.60v 4.69v 4.76v 4.80v 4.83v 4.85v 2 0v 1.63v 2.71v 3.44v 3.93v 4.25v 4.47v 4.61v 4.70v 4.76v 4.81v 4.83v 4.85v 3 0v 1.59v 2.71v 3.44v 3.93v 4.36v 4.47v 4.61v 4.70v 4.76v 4.81v 4.83v 4.85v

Table 5: Samples for the discharging process using 100KW resistor

Time:

 Trial 0s 10s 20s 30s 40s 50s 60s 70s 80s 90s 100s 110s 120s 1 5.00v 4.96v 4.92v 4.87v 4.83v 4.79v 4.75v 4.72v 4.68v 4.65v 4.61v 4.57v 4.54v 2 5.00v 4.96v 4.91v 4.87v 4.84v 4.80v 4.76v 4.72v 4.68v 4.65v 4.61v 4.58v 4.54v 3 5.00v 4.96v 4.91v 4.87v 4.83v 4.80v 4.76v 4.72v 4.68v 4.65v 4.61v 4.58v 4.54v

Table 6: Table of average voltages

##### Discharging Charging
###### Time

56k

100K

56K

100K

0s

5.00v

5.00v

0v

0v

10s

2.52v

4.96v

2.45v

1.59v

20s

1.26v

4.91v

3.75v

2.70v

30s

.61v

4.87v

4.29v

3.45v

40s

.30v

4.83v

4.55v

3.93v

50s

.15v

4.80v

4.69v

4.28v

60s

.07v

4.76v

4.76v

4.46v

70s

.04v

4.72v

4.80v

4.61v

80s

.02v

4.68v

4.82v

4.70v

90s

.01v

4.65v

4.83v

4.76v

100s

.00v

4.61v

4.84v

4.81v

110s

.00v

4.58v

4.85v

4.83v

120s

.00v

4.54v

4.85v

4.85v

Diagram 3: Graph of Voltage vs. Time for the charging phase of the 220m F capacitor and the 56KW resistor.

Diagram 4: Graph of Voltage vs. Time for the charging phase of the 220m F capacitor and the 56KW resistor.

1) Q: What should the voltage be after 1 time constant and what percent of total power is it?

A: 3.16v which is 63.2% of the original power.

Work:

2) Q: Does the percent in Q1 agree with the given drop of 63.2%?

A: Yes, there is no difference between the two calculations.

Work:

3) Q: Was the plot of Voltage vs. Time for the discharging phase expected?

A: Yes. As the charge travels through the circuit, the voltage across the capacitor should drop and the graph shows that it does.

Work:

No work required

4) Q: If a circuit has a t of 3s, how long will it take for it to become completely charged?

A: 15s

Work:

5) Q: What value of capacitor is required for it to be fully charged by a 10KW resistor in 2s?

A: 40mF

Work:

6) Q: What were the working and surge voltages of the capacitor used?

A: Working: 50v Surge: 500V

Work:

No work required

7) Q: What is leakage current?

A: Leakage current is current that flows between the two plates of the capacitor through the separating.

Work:

No work required

Conclusions

From this lab one can prove that the increase of voltage across a capacitor as a function of time while it is charging can be explained mathematically as:

V = E * (1 - e ^ -t / t). Also, the discharge of a capacitor can be described as:

V = E * e ^ -t / t. We also define t as being the time constant which is R * C. We also discover that after a period of 5 * t, the capacitor is close enough to being fully charged or fully discharged to be able to mathematically described as being so.

Attachments

A) Copies of lab recordings

B) Copies of calculations

C) Original lab handout