Question

An LCR series circuit is under resonance. If $I_m$, is current amplitude, $V_m$ is voltage amplitude, R is the resistance, Z is the impedance, $X_L$ is the inductive reactance and $X_C$ is the capacitive reactance, then

• A. $I_m=\frac{Z}{V_m}$
• B. $I_m=\frac{V_m}{X_L}$
• C. $I_m=\frac{V_m}{X_C}$
• D. $I_m=\frac{V_m}{R}$

Answer 1

Answer: (D)

$I_m=\frac{V_m}{R}$

Impedance of the circuit, $Z=\sqrt{R^2+(X_L-X_C{)}^2}$

At resonance , $X_L=X_C$

$\therefore Z=R$

$\therefore I_m=\frac{V_m}{Z}=\frac{V_m}{R}$