Question

In the circuit shown in the figure

$C_1=C,C_2=2C,C_3=3C,C_4=4C.$

Then select correct alternate

• A. Maximum potential difference is across $C_1$
• B. Minimum potential difference is across combination of $C_3$ and $C_4$
• C. Maximum potential energy is across $C_1$
• D. Maximum potential energy is across $C_2$

Answer 1

Answer: (A), (B), (C)

Maximum potential difference is across $C_1$
Minimum potential difference is across combination of $C_3$ and $C_4$
Maximum potential energy is across $C_1$

We have capacitance, $C=\frac{Q}{V}$ where $Q$ is the charge and $V$ is the potential difference.
$⟹V=\frac{Q}{C}$
Potential difference across $C_1$ is $\frac{Q}{C}$
Potential difference across $C_2$ is $\frac{Q}{2C}$
Potential difference across $C_3$ and $C_4$ is $\frac{Q}{7C}$ as effective capacitance across $C_3$ and $C_4$ is $7C$.
Potential energy across $C_1$ is $\frac{1}{2}C{V}^2$
$⟹PE=\frac{1}{2}C\times \frac{Q^2}{C^2}$
Potential energy across $C_2$ is $\frac{1}{2}2C{V}^2$
$⟹PE=\frac{1}{2}2C\times \frac{Q^2}{4C^2}=\frac{1}{2}C\times \frac{Q^2}{2C^2}$
Hence maximum potential energy is across $C_1$
Option C is correct.