Question

A circuit element shown in the figure contains a box is having either a capacitor or an inductor. The power factor of the circuit is $0.8$, while current lags behind the voltage. Find the value of $\frac{V}{100}$ where $V\text{volts}$ is the source voltage. Assume box element to be ideal.

Answer 1

Given:-
Current in the circuit $=1\text{A}$

$V_R=IR=80\text{V}$

$V_C=I{X}_C=100\text{V}$

$\therefore X_C=\frac{V_C}{I}=100\Omega$

Now, since current lags voltage, the box contains an inductor.

$\therefore \text{Power factor}=0.8$

$\frac{R}{Z}=\frac{4}{5}\Rightarrow Z=\frac{5R}{4}=100\Omega$

$\therefore Z=\sqrt{R^2+(X_L-X_C{)}^2}$

$\Rightarrow \left|\begin{array}{c}{X}_L-X_C\end{array}\right|=60\Omega$

$\Rightarrow V_X=I\left|\begin{array}{c}{X}_L-X_C\end{array}\right|=(1\times 60)=60\text{V}$

$\therefore V=\sqrt{V_R^2+V_X^2}=\sqrt{{80}^2+{60}^2}=100\text{V}$

$\therefore \frac{V}{100}=1$

$\text{Correct ans :}1$