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 potential difference across the resistor will be nearly -


$[$0.77 Mark$]$

• A. $200\text{V}$
• B. $100\text{V}$
• C. $360\text{V}$
• D. $112\text{V}$

Answer 1

The correct option is D $112\text{V}$

Impedance,

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

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

Current,

$i_{rms}=\frac{V_{rms}}{Z}=\frac{200}{20\sqrt{13}}=2.8\text{A}$

Now, potential difference across the resistor,

$V_R=i_{rms}\times R=2.8\times 40=112\text{V}$