Question

The potential difference that must be applied across the series and parallel combination of 4 identical capacitors such that the energy stored in them becomes the same. The ratio of potential difference in series to parallel combination is ______.

Options

• 1 : 1

• 2 : 1

• 4 : 1

• 8 : 1

Answer 1

The potential difference that must be applied across the series and parallel combination of 4 identical capacitors such that the energy stored in them becomes the same. The ratio of potential difference in series to parallel combination is 4 : 1.

Explanation:

The equivalent capacitance for a series combination,

C₁ = `C/4`    ...(i)

U₁ = `1/2 C_1 V_1^2`

The equivalent capacitance for a parallel combination,

C₂ = 4C    ...(iii)

U₂ = `1/2 C_2 V_2^2`    ...(iv)

Given that, U₁ = U₂

∴ `C_1 V_1^2 = C_2 V_2^2`

∴ `V_1/V_2 = sqrt (C_2/C_1)`

= `sqrt ((4 C)/(C/4)`

= `sqrt (16/1`

= `4/1`