Question

Calculate the ratio of the equivalent capacitance of the circuit when two identical capacitors are in series to that when they are in parallel?

• A. $\frac{1}{4}$
• B. $\frac{1}{2}$
• C. $1$
• D. $2$
• E. $4$

Answer 1

Answer: (A)

$\frac{1}{4}$

Let the capacitance of each capacitor be $C$.

Series combination : Equivalent capacitance $\frac{1}{C_{eq}}=\frac{1}{C}+\frac{1}{C}$ $⟹C_{eq}=\frac{C}{2}$

Parallel combination : Equivalent capacitance $C_{eq}^{\prime }=C+C=2C$

$\therefore$ $\frac{C_{eq}}{C_{eq}^{\prime }}=\frac{C/2}{2C}=\frac{1}{4}$