C. Investigation of factors affecting charging and discharging
Part A and B were repeated with the other capacitors (100μF, 220μF, 470μF, 1000μF) by using a 6V battery ( 4 x 1.5V). The readings of the galvanometer were observed and recorded, and then tabulated below.
The steps were repeated with the other voltages (1.5 V, 3.0V, 4.5V and 6.0V) by using a 470μF capacitor. The readings of the galvanometer were observed and recorded, and then tabulated below.
The step above was repeated but without discharging the capacitor after connecting each battery. The readings of the galvanometer were observed and recorded, and then tabulated below.
After that, a CRO was connected across the 1000Ω in the circuit as shown below. The CRO was set to d.c. The whole charging and discharging (connect both sides of 6V cells with a wire) current pulse was display on the CRO. The currents pulse was sketched on the same graph. The step was repeated with a 350kΩ resistor.
For 1000Ω resistor: For 350kΩ resistor:
The patterns of the two current pulses were similar. During charging, the voltage increased to a maximum at once, and then slowly decreased down to zero. During discharging, the pattern was similar to that of charging but with opposite direction. The voltage came down to negative maximum in a short time and recovered to zero slowly.
Nevertheless, the current pulse for 1000Ω resistor had a extremely higher amplitude and a shorter period than that of the current pulse for 350kΩ resistor.
Next, one more galvanometer was added in the circuit as shown below. Part A and B was repeated. The readings of both galvanometer s was observed and described.
Both galvanometers had the same readings, which went to a maximum 3.42mA at once and decreased to zero slowly during charging, and same motion with opposite charge during discharging.
Discussion:
- From Part A and B, it was found that during charging or discharging, the voltage went to it maximum and dropped down slowly. The charging and discharging motion were the same but with opposite motion.
- Factors affecting charging and discharging processes:
i) The capacitance of capacitors:
From the first table, it was found that 100/7, 220/11 …were quite similar. So it could say that the capacitance of capacitors was directly proportional to the current.
IαC or QαC
ii) The voltage across the capacitors:
Refer to the second table, with unchanged capacitance of capacitors, it was found that C=2.67V (1.5/4, 3/8…). As a result, the voltage across the capacitors was found to be directly proportional to the current.
IαC or QαC
iii) The resistance of the circuit:
From the current pulses displayed on the CRO, it was found that the pulses for 1000Ω resistor had a higher amplitude than that of the current pulse for 350kΩ resistor. So, the resistance of the circuit was found to be inversely proportional to the current.
Iα1/R or Qα1/R
Therefore, the charging and discharging currents were found to be directly proportional to the capacitance of capacitors and the voltage across the capacitors, but inversely proportional to the resistance of the circuit.
QαCV/R
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- Using a CRO to observe the charging and discharging currents, the current pulses could be observed accurately and clearly. Besides, the displays could be varied conveniently as you like.
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- Sources of error and improvement:
In the experiment, there were a few of error, which made the experimental data inaccurate.
- The apparatus given was not accurate or precise enough. (e.g. galvanometer) They may also affect the experimental data. Using better quality of apparatus instead can minimize the inaccuracy.
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There were wrong assumptions. The wires and the galvanometer had small resistance which were neglected. The 1000Ω resister had resistance <>1000Ω.They affected the experimental result actually. To reduce errors, the resistances should be considered also.
- The dry cells were not exactly 1.5V due to long time using. So, before the experiment, the voltages of dry cells should be checked by CRO first, or using new dry cells
- The scales on the galvanometers were observed by the human naked eyes. The records were inaccurate. Using a hand lens when reading, Reading the scale when the pointer is directly on top of its image in the mirror behind was important to lower the error. Apart from these, the scale was read by several people repeatedly could help the accuracy too.
Conclusion:
In this experiment, the charging and discharging currents were found to be directly proportional to the capacitance of capacitors and the voltage across the capacitors, but inversely proportional to the resistance of the circuit.