Question

For an $LCR$ series circuit with an A.C. source of angular frequency $\omega$, which statement is correct?

• A. Circuit will be capacitive if $\omega >\frac{1}{\sqrt{LC}}$
• B. Circuit will be capacitive 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

The correct option is C Power factor of circuit will be unity if capacitive reactance equals inductive reactance

Circuit will be capacitive if , total reactance =$X_L-X_C<0$

$\Rightarrow X_C>X_L\Rightarrow \frac{1}{C\omega }>L\omega \Rightarrow \omega <\frac{1}{\sqrt{LC}}$
Current will be leading the voltage if the circuit is capacitive , i.e., $\omega <\frac{1}{\sqrt{LC}}$
Power factor= $\frac{R}{Z}$ ; pf factor will be unity if $R=Z\Rightarrow X_L=X_C$ , i.e., capacitive reactance is equal to inductive reactance.