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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 μF capacitor. The capacitor is initially uncharged. The swit... 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
The maximum charge ( Q ) stored by a capacitor can be calculated using the formula:
where:
- C = capacitance in farads (F)
- V = voltage in volts (V)
Given:
- C = 47 μF = 47 \times 10^{-6} F
- V = 6 V
Substituting the values:
Thus, the maximum charge stored by the capacitor is approximately 28.2 µC.
Step 2
Add a line to the graph to show how the current now varies with time as the capacitor charges.
Answer
To show the effect of a larger resistance on the current, the line drawn on the graph should start at a lower initial current compared to the original.
- The line should rise more slowly and approach the x-axis over a longer time period, indicating a longer charging time due to the increased resistance.
Step 3
Suggest an alteration to increase the maximum energy stored by the 47 μF capacitor.
Answer
To increase the maximum energy stored in the capacitor, the student could increase the supply voltage.
This is because the energy ( E ) stored in a capacitor can be calculated by:
Increasing the voltage supplies more potential energy to the capacitor, consequently increasing the energy stored.
Step 4
Comment on the analogy between vehicles and the charging of a capacitor.
Answer
The analogy of vehicles going over a speed bump helps illustrate the concept of charging a capacitor. Just as vehicles experience a gradual increase in speed and then stabilize after the bump, a capacitor charges gradually, initially drawing a lot of current which tapers off over time.
Both scenarios depict a delayed response where an initial burst of energy decreases, representing the charging behavior of a capacitor as it approaches its maximum voltage.