A capacitor discharges through a resistance. The stored energy `U_0` in one capacitive time constant falls to

Options

A. `U_0//e^2`
B. `eU_0`
C. `U_0//e`
D. none of the above

Answer

A

Explanation

In the case of discharging, `I = I_0e^(-t//RC)`
or ` 2.5 xx 10^(-6) = (q_0)/(RC)e^(-t//RC) = 5xx10^(-6) e^(-t//RC)`
or ` e^(t//10) = 2`
Taking log on both the sides, we get
`(t)/(10) = In2 or t = 10in2 6.9 ~= 7s`