Question

Three identical capacitors, each of capacitance $C$, are wired as shown above
When both switches are closed, the equivalent capacitance is:

• A. $\frac{C}{3}$
• B. $\frac{2}{3}C$
• C. $C$
• D. $\frac{3}{2}C$
• E. $3C$

Answer 1

The correct option is B $\frac{2}{3}C$

As capacitors $C_2$ and $C_3$ are in parallel combination, therefore, equivalent capacitance of these two,

$C^{\prime }=C_2+C_3=C+C=2C$

Now $C_1$ and $C^{\prime }$ are in series, therefore

$C=\frac{C_1\times C^{\prime }}{C_1+C^{\prime }}$

$C=\frac{C\times 2C}{C+2C}=2C^2/3C=2C/3$