Question

In a series LCR circuit, the inductive reactance (X_L) is 10 Ω and the capacitive reactance (X_C) is 4 Ω. The resistance (R) in the circuit is 6 Ω. The power factor of the circuit is :

(1) \(\frac 12\)

(2) \(\frac {1}{2\sqrt2}\)

(3) \(\frac{1}{\sqrt2}\)

(4) \(\frac{\sqrt3}2\)

Answer 1

Correct option is (3) \(\frac{1}{\sqrt2}\)

We know that power factor is cos ɸ,

cos ɸ = \(\frac RZ\)......(1)

Z = \(\sqrt{R^2+(X_L-X_C)^2}\)....(2)

 (ωL – 1/ωC)

⇒ Z = \(\sqrt{6^2+(10-4)^2}\)

⇒ Z = 6√2 | cos ɸ = \(\frac 6{6\sqrt2}\)

cos ɸ = \(\frac{1}{\sqrt2}\)