A series combination of an inductor of self-inductance L, capacitor of capacitance C and resistor R is connected to an alternating voltage source of `V=V_0sinomegat`. The current through the circuit is `I=I_0sin(omegat-theta)`,where `I_0=V_0/(sqrt(R^2+(omega-1/(omegaC))^2))`and`theta=tan^-1 ""1/R(omegaL-1/(omegaC))`.
Now that, the frequency of both voltage and current is `f=omega/(2pi)` . The rms value of these parameters during one complete cycles are `V_(rms)=V_0/sqrt2`and`I_(rms)=I_0/sqrt2` respectively. These values are shown in alternating voltmeter and ammeter.
The power consumed by the circuit P=VI. The mean value i.e., the effective power of the circuit in a complete cycle is `overlineP=V_(rms)I_(rms)costheta`. This `costheta` is termed the power factor.
the power factor of the circuit is question (i) is

Options

A. zero
B. `(omegaL)/(R')`
C. `(R')/(sqrt(R'^2+omega^2L^2))`
D. `(sqrt(R'^2+omega^2L^2))/(R')`

Answer

C