Question

In a series R, L, C circuit $X_L$ = 10 , $X_C$ = 4 and $R$ = 6. Find the power factor of the circuit

• A. 1/2
• B. 3/2
• C. 5/2
• D. none of the these.

Answer 1

The correct option is D none of the these.

Given : $X_L=10$ $X_C=4$ $R=6$
Impedance of the circuit $Z=\sqrt{R^2+(X_C-X_L{)}^2}$
$⟹Z=\sqrt{6^2+(4-10)}=6\sqrt{2}$
Power factor of the circuit $\cos \varphi =\frac{R}{Z}$
$⟹\cos \varphi =\frac{6}{6\sqrt{2}}=\frac{1}{\sqrt{2}}$
Correct answer is option D.