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A student carries out an experiment to investigate the charging of a capacitor using the circuit shown - Scottish Highers Physics - Question 13 - 2022
Question 13
A student carries out an experiment to investigate the charging of a capacitor using the circuit shown. (a) Describe how the results of this experiment are obtained... show full transcript
Worked Solution & Example Answer:A student carries out an experiment to investigate the charging of a capacitor using the circuit shown - Scottish Highers Physics - Question 13 - 2022
Step 1
Describe how the results of this experiment are obtained and used to show how the voltage across the capacitor varies with time while the capacitor is charging.
Answer
To investigate the charging of the capacitor, the student closes switch S and uses a stopwatch to time the experiment. The voltage across the capacitor is measured using a voltmeter at regular time intervals after the switch is closed. The readings are taken at consistent intervals (e.g., every second) as the capacitor charges. These measurements are then plotted on a graph, where the x-axis represents time and the y-axis represents voltage. This results in a curve that shows how the voltage across the capacitor increases over time, illustrating the charging behavior in accordance with the exponential growth characteristic of RC circuits.
Step 2
Calculate the maximum energy stored by the capacitor.
Answer
The maximum energy ( E ) stored in a capacitor can be calculated using the formula:
Where:
C = 47 \mu F = 47 \times 10^{-6} F
V = 12 V
Substituting the values into the formula:
Calculating:
Thus, the maximum energy stored by the capacitor is approximately 3.384 \times 10^{-4} J.
Step 3
Suggest an alteration the student could make to this circuit to increase the maximum energy stored by the capacitor.
Answer
To increase the maximum energy stored by the capacitor, the student could increase the supply voltage. This can be achieved by adjusting the variable voltage supply to a level greater than 12 V, as long as it remains below the maximum voltage rating of the capacitor. For instance, setting the supply to 15 V would allow for greater energy storage, as the energy stored in the capacitor is proportional to the square of the voltage.