Question

In L_C oscillation , maximum charge on capacitor is $Q_0$ . The current in the circuit , when $50\%$ energy is electrical and $50\%$ is magnetic is

• A. $\frac{Q_0}{\sqrt{LC}}$
• B. $\frac{Q_0^2}{\sqrt{LC}}$
• C. $\frac{Q_0}{2\sqrt{LC}}$
• D. $\frac{Q_0}{\sqrt{2LC}}$

Answer 1

The correct option is A $\frac{Q_0}{\sqrt{LC}}$

Solution:-

Electrical energy is given by $\frac{Q^2}{2C}$

$50\%$ of it will be $\frac{Q^2}{4C}$

Magnetic energy is given by $\frac{1}{2}L{I}^2$

$50\%$ of it will be $\frac{1}{4}L{I}^2$

When Q is maximum i.e.$Q_0$ then

$\frac{Q_0^2}{2C}=\frac{Q_0^2}{4C}+\frac{1}{4}L{I}^2$

$\frac{Q_0^2}{4C}=\frac{1}{4}L{I}^2$

$I^2=\frac{Q_0^2}{LC}$

I=$\frac{Q}{\sqrt{LC}}$