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Question

A capacitor discharges through a resistance. The stored energy U0 in one capacitive time constant falls to

A
U0e2
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B
eU0
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C
U0e
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D
None of these
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Solution

The correct option is A U0e2
Let us consider charge stored in the capacitor at time (t = 0) be Q0 and energy stored in the capacitor be U0.

In case of discharging of capacitor, we know
Q=Q0etτ.......(i)
For 1 capacitive time (i.e t = τ)
Q=Q0e.....(ii)
We know that U0=Q202C.....(iii)
U=Q22C......(iv)
Using equation (iii) and (iv) in (ii) we get
U=U0e2

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