Question

Assertion : At resonance, $LCR$ series circuit have a minimum current.
Reason : At resonance, in $LCR$ series circuit, the current and e.m.f are not in phase with each other

• A. If both assertion and reason are true and reason is the correct explanation of assertion.
• B. If both assertion and reason are true but reason is not the correct explanation of assertion.
• C. If assertion is true but reason is false.
• D. If both assertion and reason are false.

Answer 1

Answer: (D)

At resonance $X_L=X_C$ or $\omega L=\frac{1}{\omega C}.$
Because of this impedance of LCR series circuit become equal to resistance of circuit
$\left(Z=\sqrt{R^2+{\left(X_L-X_C\right)}^2}\right).$
Therefore from I $=\frac{E}{Z}=\frac{E}{R},$ at resonance, current in LCR series circuit is maximum. Correspondingly phase angle is also equal to zero. Therefore emf and current are in phase in LCR series circuit.