Question

A current of $\frac{25}{\pi }Hz$ frequency is passing through an $AC$ circuit having series combination of $R=100\Omega$ and $L=2H$, the phase difference between voltage and current is _____.

• A. ${60}^{\circ }$
• B. ${90}^{\circ }$
• C. ${30}^{\circ }$
• D. ${45}^{\circ }$

Answer 1

The correct option is D ${45}^{\circ }$

Given, $f=\frac{25}{\pi }Hz$
$\therefore \omega =2\pi f=2\pi \times \frac{25}{\pi }=50rad/s$
$R=100\Omega$
and $L=2H$
The impedance of the circuit
$Z=\sqrt{R^2+{\omega }^2{L}^2}$
$=\sqrt{(100{)}^2+(50\times 2{)}^2}=\sqrt{2\times {100}^2}=100\sqrt{2}$
Now power factor, $\cos \varphi =\frac{R}{Z}=\frac{100}{100\sqrt{2}}$
$\Rightarrow \cos \varphi =\frac{1}{\sqrt{2}}$
Phase angle between voltage and current
$=\varphi ={\cos }^{-1}\left(\frac{1}{\sqrt{2}}\right)={45}^{\circ }$.