Question

A resistor of resistance $R$, capacitor of capacitance $C$ and inductor of inductance $L$ are connected in parallel to $AC$ power source of voltage ${ϵ}_0\sin \omega t$. The maximum current through the resistance is half of the maximum current through the power source. Then value of $R$ is

• A. $\frac{\sqrt{3}}{|\omega C-\frac{1}{\omega L}|}$
• B. $\sqrt{3}|\frac{1}{\omega L}-\omega L|$
• C. $\sqrt{5}|\frac{1}{\omega L}-\omega L|$
• D. None of these

Answer 1

The correct option is A $\frac{\sqrt{3}}{|\omega C-\frac{1}{\omega L}|}$

$\frac{i_{R_0}}{\sqrt{(i_{R_0}{)}^2+(i_{c_0}-i_{L_0}{)}^2}}=\frac{1}{2}$
$\Rightarrow \frac{{ϵ}_0/R}{\sqrt{({ϵ}_0/R{)}^2+{({ϵ}_0\omega C-\frac{{ϵ}_0}{\omega L})}^2}}=\frac{1}{2}$
$\Rightarrow R=\frac{\sqrt{3}}{(\omega C-\frac{1}{\omega L})}$