Question

Potential difference across capacitor of capacitance 3C when the current in the circuit is maximum is

• A. $\frac{3V_0}{4}$
• B. $\frac{V_0}{4}$
• C. $\frac{5V_0}{4}$
• D. none of these

Answer 1

The correct option is C $\frac{5V_0}{4}$

The state of the circuit 't' seconds aftre the switch is closed can be shown as in figure where 'q' is charge as a function of time and 'i' is the current in the circuit.

By applying Kirchoff's law, potential drop across any loop is zero.

Therefore,

$-\frac{C{V}_0+q}{C}-\frac{6C{V}_0+q}{3C}-L\frac{di}{dt}=0$

$-3V_0=\frac{4q}{3C}+L\frac{di}{dt}$

When current is maximum, $\frac{di}{dt}=0$

$q=-\frac{9C{V}_0}{4}$

Potential drop across the 3C capacitor then becomes

$\frac{\frac{15C{V}_0}{4}}{3C}=\frac{5V_0}{4}$