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.