Question

The power factor of a series RC circuit is $\frac{1}{\sqrt{2}}$ . If the frequency of the applied AC is halved, the power factor will be

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

$cos\varphi =\frac{R}{Z}=\frac{1}{\sqrt{2}}$ $\Rightarrow \frac{1}{\sqrt{(}{R}^2+x_x^2)}$ $=\frac{1}{\sqrt{2}}\Rightarrow X_c=R$

$X_c=\frac{1}{\omega C}$ when $\omega ‘=\frac{\omega }{2}$ $X{‘}_c=2Xc=2R$

$\therefore newcos\varphi =\frac{R}{\sqrt{R^2+4R^2}}=\frac{1}{\sqrt{5}}$