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A fully charged capacitor of capacitance 2.0 mF discharges through a 15 kΩ resistor - AQA - A-Level Physics - Question 21 - 2022 - Paper 2
Question 21
A fully charged capacitor of capacitance 2.0 mF discharges through a 15 kΩ resistor. What fraction of the stored energy remains after 1.0 minute?
Worked Solution & Example Answer:A fully charged capacitor of capacitance 2.0 mF discharges through a 15 kΩ resistor - AQA - A-Level Physics - Question 21 - 2022 - Paper 2
Step 1
What fraction of the stored energy remains after 1.0 minute?
Answer
To find the fraction of the stored energy remaining after a certain time during the discharge of a capacitor, we use the formula:
where:
- is the energy at time ,
- is the initial energy,
- is the resistance, and
- is the capacitance.
First, we calculate the time constant () using:
Given values:
- Capacitance () = 2.0 mF = 2.0 \times 10^{-3} F,
- Resistance () = 15 kΩ = 15 \times 10^{3} Ω.
Calculating the time constant:
Next, we know that after 1.0 minute (60 seconds), the fraction of energy remaining is:
rac{E(t)}{E_0} = e^{-t/RC} = e^{-60/30} = e^{-2}
Therefore, the fraction of the stored energy remaining after 1.0 minute is:
Thus, the correct choice is:
B) rac{1}{e^2}.