Question

The power factor of the circuit shown below is $1/\sqrt{2}.$ The capacitance of the circuit is equal to

• A. $400\mu F$
• B. $300\mu F$
• C. $500\mu F$
• D. $200\mu F$

Answer 1

The correct option is C $500\mu F$


$cos\varphi =\frac{1}{\sqrt{2}}=\frac{R}{Z}$

$Z=\sqrt{2}R$
$Z^2=2R^2$
$R^2+(X_L-X_c{)}^2=2R^2$
$X_L-X_c=\pm 10\Omega$
$\omega L-\frac{1}{\omega C}=\pm 10\Omega$
As $\omega =100$
$\Rightarrow (100\times 0.1-\frac{1}{100\times C})=\pm 10\Omega$
$\Rightarrow (10-\frac{1}{100C})=\pm 10\Omega$
$\frac{1}{100C}=0\text{or}20$
Possible value of $C$ is $=500\mu F$