Question

The power factor of a circuit in which a box having unknown electrical devices connected in series with a resistor of resistance $3\Omega$ is $\frac{3}{5}$. The reactance of the box is

• A. $5\Omega$
• B. $\frac{5}{3}\Omega$
• C. $4\Omega$
• D. $\frac{4}{3}\Omega$

Answer 1

The correct option is C $4\Omega$

We have,
Power factor $\cos \varphi =\frac{R}{Z}=\frac{3}{5}$
$\Rightarrow 5R=3Z$

$\Rightarrow 5R=3\sqrt{R^2+X^2}$
($X:$ Net reactance of the box)
$25R^2=9R^2+9X^2$
$16R^2=9X^2$
$X=\frac{4}{3}R$
$X=\frac{4}{3}\times 3$
$X=4\Omega$