Question

A series LCR circuit is connected across an AC supply of frequency $f$. The resonant frequency of the circuit is $f_r$. The current will lag behind the voltage when -

• A. $f=0$
• B. $f=f_r$
• C. $f>f_r$
• D. $f<f_r$

Answer 1

The correct option is C $f>f_r$

The current will lag behind the voltage when inductive reactance is greater than capacitive reactance.

$\Rightarrow X_L>X_C$

$\Rightarrow \omega L>\frac{1}{\omega C}$

​​​​​​​$\Rightarrow {\omega }^2>\frac{1}{LC}$

$\Rightarrow \omega >\frac{1}{\sqrt{LC}}$

$\Rightarrow \frac{\omega }{2\pi }>\frac{1}{2\pi \sqrt{LC}}$

$\Rightarrow f>\frac{1}{2\pi \sqrt{LC}}$

$\Rightarrow f>f_r$

Hence, option $\left(C\right)$ is the correct answer.