Question

A resistor r, and inductor l and a capacitor c are connected in series to a source of frequency n. If the resonant frequency is nr, then the current lags behind voltage when

Answer 1

answer : $\eta > \eta_r$,

explanation : The current will leg behind the voltage when, reactance of inductor is more than reactance of conductor.

reactance of inductor , $X_L=\omega L$

reactance of capacitor, $X_C=\frac{1}{\omega C}$

where, $\omega$ is angular frequency, L is inductance of inductor and C is capacitance of capacitor.

so, $X_L > X_C$

or, $\omega L > \frac{1}{\omega C}$

or, $\omega^2 > \frac{1}{LC}$

or, $\omega > \frac{1}{\sqrt{LC}}$

or, $\eta > \frac{1}{2\pi\sqrt{LC}}$

or, $\eta > \eta_r$,

where $\eta_r$ is resonant frequency.