Question

In the circuit, as shown in the figure, if the value of R.M.S current is 2.2 A, the power factor of the box is

• A. $\frac{1}{\sqrt{2}}$
• B. $1$
• C. $\frac{\sqrt{3}}{2}$
• D. $\frac{1}{2}$

Answer 1

The correct option is A

$\frac{1}{\sqrt{2}}$

$Z=\frac{V}{i}\Rightarrow R^2+(X_L+X_C{)}^2=(\frac{220}{2.2}{)}^2\Rightarrow X_L=X_C=100\Omega ;$ Z of the box $=\sqrt{R^2+X_C^2}$
$\Rightarrow Z=100\sqrt{2}$. Power factor of the box $=\frac{R}{Z}.$