Question

A series $\text{LCR}$ circuit connected across $(200\text{V},60\text{Hz})$ source. It consists of a capacitor of capacitive reactance $30\Omega$, a non-inductive resistor of $40\Omega$ and an ideal inductor of inductive reactance $90\Omega$ as shown in the figure. The average power dissipated in the circuit is nearly



​​​​​​​$[$0.77 Mark$]$

• A. $308\text{W}$
• B. $50\text{W}$
• C. $240\text{W}$
• D. $80\text{W}$

Answer 1

The correct option is A $308\text{W}$

Impedance,

$Z=\sqrt{R^2+(X_L-X_C{)}^2}$

$=\sqrt{{40}^2+(90-30{)}^2}=20\sqrt{13}\Omega$

Current,

$i_{rms}=\frac{V_{rms}}{Z}=\frac{200}{20\sqrt{13}}=\frac{10}{\sqrt{13}}\text{A}$

Now, average power,

$P_{avg}=V_{rms}{I}_{rms}\cos \varphi =V{i}_{rms}\times \frac{R}{Z}$

$\Rightarrow P_{avg}=200\times \frac{10}{\sqrt{13}}\times \frac{40}{20\sqrt{13}}=308\text{W}$