charging a capacitor at a constant rate(C08)
School
True Light Girls' College
Mark
Name
Tam Teresa (???)
Class (Class No.)
6S (22)
/10
Group No.
3
Date (dd-mm-yy)
20-05-2009
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AL Physics TAS - Experimental Worksheet
C08 - Charging a capacitor at a constant rate
Time Allowed
2 periods
Objective
To investigate how the charge on a capacitor is related to the potential difference applied across it by charging the capacitor at a constant rate.
Apparatus
* Capacitor (electrolytic type) 500µF
* Microammeter 100µA
* Potentiometer 100k?
* Clip component holder
* Stop-watch
* CRO (Cathode Ray Oscillator)
* Connecting leads
Theory
From definition, the capacitance C of a capacitor is found from
C=Q/V
where Q is the charge stored on the capacitor and V is the potential difference across it.
==> Q = CV
==> = C
If a capacitor is charged up at a constant rate, i.e. = I , where I is a constant , then is also constant.
Hence the potential difference across the capacitor increases linearly with time.
Procedure
. Connect up the circuit as shown in Fig. (a). Set the CRO to d.c. and the sensitivity to 1V/cm.
2. Set the time base to any high value so that a steady horizontal trace is displayed. Shift the trace to the bottom of the screen.
3. Short out the capacitor by connecting a lead across it and adjust the 100k? potentiometer for a suitable current, 80µA.
4. Remove the shorting lead and the capacitor will charge up. Note what happens to the microammeter reading and the CRO trace.
5. Repeat the procedure but this time start the stop-watch and continuously adjust the potentiometer to keep the current, 70µA, constant as the capacitor charges up.
6. Measure the times for the CRO trace to move up by 1cm, 2 cm, 3 cm, 4 cm, 5cm and 6cm.These are the times for the pd across the capacitor to reach 1V, 2V, 3V, 4V, 5V and 6V.
7. Tabulate the results.
Results
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4. Remove the shorting lead and the capacitor will charge up. Note what happens to the microammeter reading and the CRO trace.
5. Repeat the procedure but this time start the stop-watch and continuously adjust the potentiometer to keep the current, 70µA, constant as the capacitor charges up.
6. Measure the times for the CRO trace to move up by 1cm, 2 cm, 3 cm, 4 cm, 5cm and 6cm.These are the times for the pd across the capacitor to reach 1V, 2V, 3V, 4V, 5V and 6V.
7. Tabulate the results.
Results
In step 4, on removing the shorting lead, the microammeter reading decreases and the CRO trace moves up, but not at a steady rate.
Constant Charging Current = 70µA
Potential difference (p.d.) across the capacitor V/V
2
3
4
5
6
t1/s
6.5
4.0
22.0
30.0
38.8
47.0
t2/s
6.8
4.0
21.8
30.0
38.8
47.0
t3/s
6.4
4.2
22.0
30.0
38.8
46.9
t4/s
6.6
4.0
21.8
30.0
38.9
46.5
t5/s
6.5
4.4
22.0
30.1
38.2
47.0
t6/s
7.0
4.5
22.0
30.5
39.0
47.4
t7/s
6.8
4.2
21.8
29.9
38.1
46.5
t8/s
6.4
4.3
22.0
29.9
38.0
46.2
t9/s
6.5
4.0
21.8
29.8
38.7
46.6
t10/s
6.9
4.1
22.0
30.0
39.0
47.0
t11/s
7.0
4.6
22.1
30.9
38.8
47.1
Average value of Time t/s
6.7
4.2
21.9
30.1
38.6
46.8
The graph of V against t is a straight line passing through origin showing that the p.d. across the capacitor is directly proportional to time (V?t).
Analysis
For a constant current, the charge delivered to the capacitor is directly proportional to time.
Q?t (Q = It)
From the result of the experiment, the p.d. across the capacitor is directly proportional to time.
V?t
As a result, the charge delivered to the capacitor is directly proportional to the p.d. across it.
Q?V
Assumptions
. The capacitor has been fully discharged before every charging.
2. The charging current is constant when the capacitor is charging.
3. The reading of times taken by the observer is exactly the same as the times for the p.d. across the capacitor to reach 1V, 2V, 3V, etc.
Precautions of the experiment
. A correct scale of ammeter should be chosen. The measured value of current may be out of range of ammeter if inappropriate ammeter is chosen.
2. As we use the stop-watch to take the times for the p.d. across the capacitor to reach 1V, 2V, 3V,etc, the reaction time of the observer plays large part. Therefore, we should have the same person for timing to prevent great time lag within same p.d. across capacitor.
3. We should ensure that the capacitor has been fully discharged before being charged up by referring to the 0V reading of CRO.
4. We should use a smaller constant charging current by adjusting the resistor to greater resistance, the capacitor will discharge much slowly, and hence, the charging process can be more easily observed, the results of times will be more accurate.
5. Before every charging, we should set the variable resistor to maximum resistance. Otherwise, the current flowing through the circuit may be too large that will destroy the microammeter.
6. We should adjust the intensity and focus of the CRO trace to attain better observation of voltage reading on CRO.
7. We should remove the shorting lead and start the stop-watch at the same time. These two tasks must be done by the same person due to different reaction time of different people.
8. To ensure that the shorting lead is removed and the stop-watch is started at the same time, the shorting lead should be easily removed, which can be done by connecting it to the clip component holder before removal.
9. Repeat the experiment for few more times to take the average value of the times for the CRO trace to move up by 1 cm, 2 cm, 3 cm, etc. As a result, the reaction time of the observer who operates the stop-watch will be less significant.
Sources of Error
. The charging current is difficult to maintain constant as the pointer of the ammeter always vibrates with small amplitude.
2. The observer who operate the stop-watch possess reaction time when timing, therefore, the time taken by her is not exactly equal to the times for the p.d. across the capacitor to reach 1V, 2V, 3V, etc.
3. The capacitor may not fully discharged before charging, thus affect the results of times for the p.d. across the capacitor to reach 1V, 2V, 3V, etc.
4. It is too difficult to observe both stop-watch and reading of CRO trace. Thus, there may exist time lag and affects the results.
Improvements
. "Dry Runs" before actual measurement.
2. Use advance stop-watch which can take several readings at once.
3. Use video camera to capture the position of horizontal CRO trace against time. Thus, the reaction time of observer does not play a part in the experiment. The results of times are much more accurate.
Limitations
. The laboratory does not have advance stop-watch.
2. We do not have enough time to do several more times to take the average value of time to make the reaction time less significant.
Comments
This experiment has errors that make our experimental results inaccurate. Fortunately, I and my partner do cooperate well to minimize the error. Also, we conduct the experiment safely and the process is holistically fluent.
Conclusion
The charge on a capacitor is directly proportional to the potential difference applied across it by charging the capacitor at a constant rate.