In the circuit shown in the figure, if the power consumed by the 5 Ω resistor is 10 W, then the power factor of the circuit is

Concept:

The given circuit is R-L series circuit. Therefore current will be equal in all the element.

Given, Power consumed by 5 Ω resister is 10 W.

i.e, \(\rm I^2_{rms}=10\)

⇒ \(\rm I^2_{rms}=\frac{10}{5}=2\ A\)

⇒ I_rms = √2 A

V_s = 50 sin ωt

V_srms = 50 / √2 

∴ \(\rm z=\frac{V_{srms}}{I_{rms}}=\frac{50/√{2}}{√{2}} Ω=25\ Ω\)

r_eq = 5 + 10 = 15 Ω

∴ \(\rm \cos\phi=\frac{R_{eq}}{z_{eq}}=\frac{15}{25}=0.6\)

Therefore, correct option will be 3.