Question

In the given circuit, current in resistance $R$ is $1A$, then

• A. $V_s=5\text{volt}$
• B. Impedance of network is $5\Omega$.
• C. Power factor of given circuit is 0.6 lagging.
• D. Power factor of given circuit is 0.6 leading.

Answer 1

Answer: (A), (B), (C)

The correct options are
A $V_s=5\text{volt}$
B Impedance of network is $5\Omega$.
C Power factor of given circuit is 0.6 lagging.

Here $I=1\text{A}$ given
So resistance $R=\frac{V_R}{I}=\frac{3}{1}=3\Omega$
Similarly,
Reactance of inductor $X_L=\frac{V_L}{I}=\frac{8}{1}=8\Omega$
Reactance of capacitor $X_C=4\Omega$
So, impedence $Z=\sqrt{R^2+(X_L-X_C{)}^2}=\sqrt{3^2-(8-4{)}^2}=5\Omega$
Hence option B is correct.

Now, voltage supplied $V_s=I\times Z=1\times 5=5\text{V}$
Hence option A is correct.

And we know power factor ($\cos \varphi$) is given by
$\cos \varphi =\frac{R}{Z}=\frac{3}{5}=0.6$
$\because V_L>V_C$ , $I$ lags $V$
Hence option C is also correct.