For an LCR series circuit with an aac source of angular frequency `omega`.

Options

A. circular will be capacitive if `omegagt(1)/(sqrt(LC))`
B. circular will be inductive if `omega=(1)/(sqrt(LC))`
C. Power factor of circuit will be unity if capacitive reactance equals inductive reactance
D. circular will be leading voltage if `omegagt(1)/(sqrt(LC))`

Answer

C

Explanation

The circuit will have inductive nature if
`omega gt (1)/(sqrt(LC))(omega L gt(1)/(sqrt(LC)))`
Hence, (a) is false. Also if circuit has inductive nature, The current will lag behind voltage, Hence (d) is also false.
If `omega =(1)/(sqrt(LC)) (omegaL=(1)/(omega C))`, the circuit will have resistance nature, Hence (b) is false.
Power factor, `cos (phi) = (R )/(sqrt(R^(2)+ (omegaL=(1)/(omega C))^(2))=1`
If `omega L =(1)/(omega C). Hence (c) is true.