Question

A resistance of $300\Omega$ and an inductance of $\frac{1}{\pi }$ henry are connected in series to a A.C. voltage of 20 volts and 200 Hz frequency. The phase angle between the voltage and current is :-

• A. ${\tan }^{-1}\left(\frac{4}{3}\right)$
• B. ${\tan }^{-1}\left(\frac{3}{4}\right)$
• C. ${\tan }^{-1}\left(\frac{3}{2}\right)$
• D. ${\tan }^{-1}\left(\frac{2}{3}\right)$

Answer 1

The correct option is A ${\tan }^{-1}\left(\frac{4}{3}\right)$

Given $R=300\Omega ,L=\frac{1}{\pi }H,f=200Hz$

$w=2\pi f=400\pi$

So $\tan \varphi =\frac{V_L}{V_R}$

Also, $V_L=I_{o}wL=I_{o}400\pi .\frac{1}{\pi }=400I_o$

$V_R=I_{o}R=300I_o$

$\Rightarrow \tan \varphi =\frac{400I_o}{300I_o}=\frac{4}{3}$