Question

The percentage increase in the impedance of an a.c circuit, when its power factor changes form $0.866$ to $0.5$ is (if resistance of the circuit remains constant)

• A. $73.2\%$
• B. $86.6\%$
• C. $90.8\%$
• D. $66.6\%$

Answer 1

The correct option is A $73.2\%$

We know that power factor $=\frac{R}{Z}$
Here, $Z$ is the impedance of the circuit.

As power factor changes from $0.866$ to $0.5$, impedance changes from $\frac{R}{0.866}$ to $\frac{R}{0.5}$.

So, $\%\text{increase of impedance}$
$=\frac{\frac{R}{0.5}-\frac{R}{0.866}}{\frac{R}{0.866}}\times 100=73.2\%$