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)

$I_{m} = \frac{V_{m}}{R}$

Answer 2

: Impedance of the circuit,

$Z = \sqrt{R^{2} + (X_{L} - X_{C})^{2}}$

At resonance, $X_{L} = X_{C}$

$\therefore Z = R$

$\therefore I_{m} = \frac{V_{m}}{Z} = \frac{V_{m}}{R}.$