Question

A solenoid of inductance $L=1\text{H}$ is connected across an AC supply of voltage, $V=100\sin \left(20t\right)$. The maximum energy stored in the solenoid is -

• A. $25.5\text{J}$
• B. $12.5\text{J}$
• C. $15.5\text{J}$
• D. $17.5\text{J}$

Answer 1

The correct option is B $12.5\text{J}$

Peak current in the circuit,

$I_0=\frac{V_0}{X_L}=\frac{V_0}{\omega L}$

$\Rightarrow I_0=\frac{100}{20\times 1}=5\text{A}$

Therefore, maximum energy stored in the solenoid,

$E_0=\frac{1}{2}L{I}_0^2=\frac{1}{2}\times 1\times 5^2=12.5\text{J}$

Hence, option $\left(B\right)$ is the correct answer.