Question

For a LCR series circuit with an A.C. 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 wiU be leading voltage if $\omega >\frac{1}{\sqrt{LC}}$

Answer 1

Answer: (C)

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.