Two equal capacitors are first connected in series and then in parallel. The ratio of the equivalent capacities in the two cases will be:

Question

Two equal capacitors are first connected in series and then in parallel. The ratio of the equivalent capacities in the two cases will be: (A) 4: 1 (B) 2: 1 (C) 1: 4 (D) 1: 2

Tardigrade Admin · Accepted Answer

For series combination

(1/Ceq1) = (1/C) + (1/C) ⇒ Ceq1 = (C/2) For parallel combination

Ceq2 = C + C ⇒ Ceq2 = 2C ⇒ (Ceq1/eq2) =(C/2/2C)= (1/4) = 1: 4

Q. Two equal capacitors are first connected in series and then in parallel. The ratio of the equivalent capacities in the two cases will be:

4: 1

2: 1

1: 4

1: 2

For series combination

$\frac{1}{C _{e q_{1}}} = \frac{1}{C} + \frac{1}{C}$
$\Rightarrow C_{e q_{1}} = \frac{C}{2}$
For parallel combination

$C_{e q_{2}} = C + C$
$\Rightarrow C_{e q_{2}} = 2 C$
$\Rightarrow \frac{C _{e q_{1}}}{e q _{2}} = \frac{C /2}{2 C} = \frac{1}{4} = 1 : 4$