Question

A capacitor is discharging through a resistor R. Consider in time t₁, the energy stored in the capacitor reduces to half of its initial value and in time t₂, the charge stored reduces to one-eighth of its initial value. The ratio t₁/t₂ will be ______.

Options

• 1/2

• 1/3

• 1/4

• 1/6

Answer 1

A capacitor is discharging through a resistor R. Consider in time t₁, the energy stored in the capacitor reduces to half of its initial value and in time t₂, the charge stored reduces to one-eighth of its initial value. The ratio t₁/t₂ will be 1/6.

Explanation:

When the energy in a discharging capacitor is reduced to half, the charge becomes `1/sqrt2` times its initial value.

Now, `(1/2)^{1"/"2} = e^{-t_1"/"tau}` ......(1)

Similarly, `(1/2)^3 = e^{-t_2"/"tau}` ............(2)

When we divide equation (1) by (2), we get:

`t_1/t_2 = 1/6`