Two identical capacitors are first connected in series and then in parallel. The ratio of equivalent capacitance is

Question

Two identical capacitors are first connected in series and then in parallel. The ratio of equivalent capacitance is (A)  1:1  (B)  1:2  (C)  1:3  (D)  1:4

Tardigrade Admin · Accepted Answer

Capacitor in series (1/Cs)=(1/C)+(1/C)=(2/C) ⇒ Cs=(C/2) Capacitor in parallel Cp=C+C=2 C ∴ (Cg/Cp)=(C/2 × 2 C) =(1/4)

Q. Two identical capacitors are first connected in series and then in parallel. The ratio of equivalent capacitance is

$1 : 1$

$1 : 2$

$1 : 3$

$1 : 4$

Capacitor in series $\frac{1}{C _{s}} = \frac{1}{C} + \frac{1}{C} = \frac{2}{C}$
$\Rightarrow C_{s} = \frac{C}{2}$ Capacitor in parallel
$C_{p} = C + C = 2 C$
$∴ \frac{C _{g}}{C _{p}} = \frac{C}{2 \times 2 C}$
$= \frac{1}{4}$