Question

In an $LRC$ circuit, the power factor changes from $\frac{1}{2}$ to $\frac{1}{4}$ then, what is the increase in impedance (the resistance of the resistor in the circuit is constant) ?

• A. $20\%$
• B. $50\%$
• C. $25\%$
• D. $100\%$

Answer 1

The correct option is D $100\%$

We know that power factor is given by,

$\cos \varphi =\frac{R}{Z}$

Here, the impedance, $Z$ of the circuit is changing. But $R$ remains constant.

$\therefore \cos {\varphi }_1=\frac{R}{Z_1}=\frac{1}{2}\Rightarrow Z_1=2R$

And, $\cos {\varphi }_2=\frac{R}{Z_2}=\frac{1}{4}\Rightarrow Z_2=4R$

$\Delta Z=Z_2-Z_1=2R$

$\%$ Increase in impedance,

$=\frac{\Delta Z}{Z_1}\times 100\%$

$=\frac{2R}{2R}\times 100\%$

$=100\%$

Hence, option $\left(D\right)$ is correct.