Question

When resonance is produced in a series $LCR$ circuit, then which of the following is not correct?

• A. Current in the circuit is in phase with the applied voltage.
• B. Inductive and capacitive reactances are equal.
• C. If $R$ is reduced, the voltage across capacitor will increase.
• D. Impedance of the circuit is maximum.

Answer 1

Answer: (D)

If $f_0$ is the resonance frequency corresponding to resonant angular frequency ${\omega }_0$, then $f_0=\frac{{\omega }_0}{2\pi }=\frac{1}{2\pi \sqrt{LC}}\left(\because {\omega }_0=\frac{1}{\sqrt{LC}}\right)$
The above eqn. is called the condition for resonance in the $LCR$ circuit. Figure shows the variation of current with frequency of the source. It follows that for $f=f_0$, the current in the circuit is maximum and hence, impedance of the circuit is minimum.