Question

A sinusoidal voltage of peak value $283\, V$ and angular frequency $320/s$ is applied to a series $LCR$ circuit. Given that $R = 5 \, \Omega , L = 25 \, mH $ and $C=1000 \, \mu F$. The total impedance, and phase difference between the voltage across the source and the current will respectively be :

• A. $10 \Omega $ and $\tan^{-1} \left( \frac{5}{3} \right)$
• B. $7 \Omega$ and $45^{\circ}$
• C. $10 \Omega $ and $\tan^{-1} \left( \frac{8}{3} \right)$
• D. $7 \Omega $ and $\tan^{-1} \left( \frac{5}{3} \right)$

Answer 1

Answer: (B)

$e_{0}=283$ volt $\omega=320$
$x_{L}=320\times25\times10^{-3}=8\,\Omega$
$x_{C}=\frac{1}{\omega C}=\frac{1}{320\times1000\times10^{-6}}$
$=\frac{1000}{320}=3.1\,\Omega$
$R=5\,\Omega$
$Z=\sqrt{R^{2}+\left(X_{L}-X_{C}\right)^{2}}=\sqrt{50}=7\,\Omega$
$tan\,\phi=\frac{X_{L}-X_{C}}{R}$
$=1\,\phi=45^{\circ}$