Question

By what percentage the impedance in an ac series circuit should be increased so that the power factor changes from (1/2) to (1/4) (when r is constant) ?

Answer 1

Power factor of any AC circuit is given by

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

so for two cases where resistance R is constant

$\frac{R}{Z_1} = \frac{1}{2}$

$Z_1 = 2R$

also we have

$\frac{R}{Z_2} = \frac{1}{4}$

$Z_2 = 4R$

now the percentage change in impedence is given by

$percentage = \frac{Z_2 - Z_1}{Z_1}*100$

$percentage = \frac{4R - 2R}{2R}* 100 = 100$

so there is 100% change in the impedence of the given AC circuit