Question

A coil of self - inductance $\left(\frac{1}{\pi }\right)$H is connected in series with a 300$\Omega$ resistance. A voltage of 200V at frequency 200Hz is applied to this combination. The phase difference between the voltage and the current will be

• A. $ta{n}^{-1}\left(\frac{4}{3}\right)$
• B. $ta{n}^{-1}\left(\frac{3}{4}\right)$
• C. $ta{n}^{-1}\left(\frac{1}{4}\right)$
• D. $ta{n}^{-1}\left(\frac{5}{4}\right)$

Answer 1

Answer: (A)

$ta{n}^{-1}\left(\frac{4}{3}\right)$

$X_L=\omega L$

$=2\pi fL$

$=2\pi \left(200\right)\frac{1}{\pi }$

$=400$

$R=300$

phase difference $\theta ={tan}^{-1}\left(\frac{X_C}{R}\right)$

$={tan}^{-1}\left(\frac{400}{300}\right)$

$={tan}^{-1}\left(\frac{4}{3}\right)$