Question

The percentage increase in the impedance of an ac circuit, when its power factor changes from $0.866$ to $0.5$ is- (Resistance constant)

• A. $73.3\%$
• B. $86.6\%$
• C. $90.8\%$
• D. $66.6\%$

Answer 1

The correct option is A $73.3\%$

Power factor is, $\cos \varphi =\frac{R}{Z}$

Initially, the power factor is,

$\cos {\varphi }_1=\frac{R}{Z_1}=0.866$

$\Rightarrow Z_1=\frac{R}{0.866}=1.154R$

Finally, the power factor is,

$\cos {\varphi }_2=\frac{R}{Z_2}=0.5$

$\Rightarrow Z_2=2R$

Now percentage increase in the impedance of an ac circuit is,

$\Rightarrow \text{percentage increase in}Z=\frac{Z_2-Z_1}{Z_1}\times 100$

$\therefore \text{percentage increase in}Z=\frac{\left(2R\right)-\left(1.154R\right)}{\left(1.154R\right)}\times 100=73.3\%$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\left(A\right)$ is the correct answer.