Question

For an $LCR$ series circuit with an ac source of angular frequency $\omega$,

• A. circuit will be capacitive if $\omega >\frac{1}{\sqrt{LC}}$
• B. circuit will be inductive if $\omega =\frac{1}{\sqrt{LC}}$
• C. power factor of circuit will be unity if capacitive reactance equals inductive reactance
• D. current will be leading voltage if $\omega >\frac{1}{\sqrt{LC}}$

Answer 1

Answer: (C)

The circuit will have inductive nature if
$\omega >\frac{1}{\sqrt{LC}}\left(\omega L>\frac{1}{\sqrt{LC}}\right)$
Hence (a) is false. Also, if circuit has inductive nature, the current will lag behind voltage. Hence, (d) is also false.
If $\omega =\frac{1}{\sqrt{LC}}\left(\omega L=\frac{1}{\omega C}\right)$, the circuit will have resistance nature. Hence, (b) is false.
Power factor, $\cos \varphi =\frac{R}{\sqrt{R^2+{\left(\omega L-\frac{1}{\omega C}\right)}^2}}=1$
If $\omega L=\frac{1}{\omega C}.$ Hence, (c) is true.