Question

The potential differences that must be applied across the parallel and series combination of 3 identical capacitors are such that the energy stored in them becomes the same. The ratio of potential difference in parallel to series combination is ______

Options

• `1/3`

• `1/4`

• `1/8`

• `1/6`

Answer 1

The potential differences that must be applied across the parallel and series combination of 3 identical capacitors are such that the energy stored in them becomes the same. The ratio of potential difference in parallel to series combination is `underline(1/3)`.

Explanation:

Let C be the capacity of each capacitor. The equivalent capacitance of three capacitors in parallel combination will be C_p = 3C and in series combination C_s = `C/3`

Let V_P be the potential difference in parallel combination and V_s in series combination then the energy stored in the same in the two cases.

∴ `1/2C_p V_p^2 = 1/2C_s V_s^2`

∴ `(V_p^2)/(V_s^2) = C_s/C_p = C/3 . 1/(3C) = 1/9`

∴ `V_p/V_s = 1/3`