Question

A sinusoidal voltage $V ( t )=210 \sin 3000 t$ volt is applied to a series $LCR$ circuit in which $L =10$ $mH , C =25 \mu F$ and $R =100\, \Omega$. The phase difference $(\Phi)$ between the applied voltage and resultant current will be :

• A. $\tan ^{-1}(0.17)$
• B. $\tan ^{-1}(9.46)$
• C. $\tan ^{-1}(0.30)$
• D. $\tan ^{-1}(13.33)$

Answer 1

Answer: (A)

$X _{ L }=10^{-2} \times 3000=30\, \Omega$
$X _{ C }=\frac{1}{3000 \times 25 \times 10^{-6}}=\frac{40}{3} \Omega$
$X = X _{ L }- X _{ C }$
$=30-\frac{40}{3}=\frac{50}{3}$
$\tan \delta=\frac{ X }{ R }=\frac{50}{3 \times 100}=\frac{1}{6}$
$\delta=\tan ^{-1}\left(\frac{1}{6}\right)=\tan ^{-1}(0.17)$