Question

In the adjoining ac circuit, the voltmeter whose reading will be zero at resonance is

Answer 1

Impedance and voltage at resonace

1. We know the impedance of an LCR circuit is expressed by the form, $Z=\sqrt{\left(R^2+{\left(\omega L-\frac{1}{\omega c}\right)}^2\right)}$, where R is the resistance, $\frac{1}{\omega c}$ is the capacitive reactance, and $\omega L$is the inductive reactance.
2. But at resonance, the capacitive reactance = inductive reactance, i.e, $\frac{1}{\omega c}=\omega L$.
3. So at resonance total impedance = total resistance, i.e, Z = R.
4. From Ohm's law, voltage = IR, but net impedance across the inductor and capacitor is zero. So at resonance net voltage across the inductor and capacitor is zero.

Diagram

Therefore, at resonance net voltage across the inductor and capacitor is zero.