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A student investigates the charging of a capacitor - Scottish Highers Physics - Question 13 - 2019
Question 13
A student investigates the charging of a capacitor. The student sets up the circuit as shown using a 47.1 µF capacitor. The capacitor is initially uncharged. The sw... show full transcript
Worked Solution & Example Answer:A student investigates the charging of a capacitor - Scottish Highers Physics - Question 13 - 2019
Step 1
Calculate the maximum charge stored by the capacitor.
Answer
To find the maximum charge stored by a capacitor, we use the formula:
Where:
- is the charge in coulombs
- is the capacitance in farads (F)
- is the voltage in volts (V)
In this case:
Thus, substituting these values into the formula, we get:
Therefore, the maximum charge stored by the capacitor is approximately .
Step 2
Add a line to the graph to show how the current varies with time.
Answer
When the resistor is replaced with one of greater resistance, the charging time increases, resulting in a lower initial current as the capacitor charges. The line on the graph should start at a lower value on the current axis and show a more gradual decline compared to the previous graph, indicating a longer charging period.
Step 3
Suggest an alteration to increase the maximum energy stored by the 47 µF capacitor.
Answer
To increase the maximum energy stored by the capacitor, the student could increase the supply voltage. Since the energy stored in a capacitor is given by:
Increasing the voltage (V) will significantly increase the energy, as it is squared in the formula.
Step 4
Comment on the analogy of vehicles during a speed bump.
Answer
The analogy of vehicles encountering a speed bump resembles the charging of a capacitor in that, initially, when the vehicle (representing the capacitor) hits the bump, there is a sudden change in conditions leading to an initial surge of energy (current). As the vehicle passes over the bump (charging process), the movement gradually smoothens, similar to the way the current decreases as the capacitor approaches its maximum charge. This analogy highlights how external factors affect the behavior of a system over time.