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The initial potential difference across a capacitor is $V_0$ - AQA - A-Level Physics - Question 22 - 2019 - Paper 2

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The initial potential difference across a capacitor is $V_0$. The capacitor discharges through a circuit of time constant $T$. The base of natural logarithms is $e$.... show full transcript

Worked Solution & Example Answer:The initial potential difference across a capacitor is $V_0$ - AQA - A-Level Physics - Question 22 - 2019 - Paper 2

Step 1

What is the potential difference across the capacitor after time $T$?

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Answer

To find the potential difference across the capacitor at time TT, we can use the formula for the discharging of a capacitor, which is given by:

V(t)=V0e−t/TV(t) = V_0 e^{-t/T}

Substituting tt with TT, we have:

V(T)=V0e−T/T=V0e−1=V0eV(T) = V_0 e^{-T/T} = V_0 e^{-1} = \frac{V_0}{e}

Therefore, the potential difference across the capacitor after time TT is V0e\frac{V_0}{e}, which corresponds to option B.

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