Question

Twelve capcitors each having a capacitance $C$, are connected to form a cube. Find the equivalent capacitance of the cube along its body diagonal?

• A. $\frac{8}{3}C$
• B. $\frac{6}{5}C$
• C. $\frac{4}{3}C$
• D. $\frac{12}{7}C$

Answer 1

The correct option is B $\frac{6}{5}C$


Suppose the points $\text{A}$ and $\text{B}$ are connected to a battery.

Suppose the positive termainal of the battery supplies a charge is divided on the three plates connected to $\text{A}$.

By applying symmetry and charge conservation the charge on each capacitor is obtained as shown in the figure.



Potential difference between $\text{AG}$ is given by

$V_{AG}=V_{AE}+V_{CH}+V_{HG}=V$

If $C_{eqv}$ is equivalent capacitance across the diagonal $\text{AG}$, then

$\frac{Q}{C_{{}_{eqv}}}=\frac{\frac{Q}{3}}{C}+\frac{\frac{Q}{6}}{C}+\frac{\frac{Q}{3}}{C}$

$\Rightarrow \frac{1}{C_{eqv}}=\frac{2+1+2}{6C}$

$\therefore C_{eqv}=\frac{6}{5}C$

Hence, option (b) is correct answer.