Question

If the power factor of an AC RL circuit changes from $\frac{1}{2}$ to $\frac{1}{4}$ keeping resistance constant, what is the percentage change in the impedance of the circuit?

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

Answer 1

The correct option is D $100\%$

We know that, power factor,

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

Here, the impedance of the circuit is changing, but the resistance remains constant.

So,

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

and,

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

Now,

$\Delta Z=Z_2-Z_1=4R-2R=2R=Z_1$

Therefore, percentage change in the impedance is,

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

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