Photo AI
An uncharged 220 µF capacitor is connected in a circuit as shown - Scottish Highers Physics - Question 13 - 2017
Question 13
An uncharged 220 µF capacitor is connected in a circuit as shown. The 12V battery has negligible internal resistance. (a) Switch $S_1$ is closed and the capacitor ... show full transcript
Worked Solution & Example Answer:An uncharged 220 µF capacitor is connected in a circuit as shown - Scottish Highers Physics - Question 13 - 2017
Step 1
Calculate the initial charging current.
Answer
To find the initial charging current when the switch is closed, we can apply Ohm’s Law, which states that:
Here, we have:
- Voltage,
- Resistance,
Rearranging the formula to find current gives:
Substituting the known values:
Calculating this yields:
Thus, the initial charging current is approximately .
Step 2
Explain why the time for the capacitor to fully charge is less than in part (a).
Answer
When switch is closed and the capacitor is charged, the initial current is at its maximum because the capacitor behaves like a short circuit at that moment.
Once the capacitor is at a voltage close to the supply voltage, the charging current decreases significantly.
However, when switch is closed immediately after discharging the capacitor, the equivalent resistance of the circuit becomes less than when charging through a 6800 Ω resistance alone.
This lesser resistance results in a greater initial charging current when switch is closed again. Since the current is greater, the capacitor charges faster, leading to a shorter time to fully charge than in part (a).