Question

A sinusoidal voltage of peak value $283V$ and angular frequency $320/s$ is applied to a series $LCR$ circuit. Given that $R=5\Omega ,L=25mH$ 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 $\omega =320$
$x_L=320\times 25\times 10^{-3}=8\Omega$
$x_C=\frac{1}{\omega C}=\frac{1}{320\times 1000\times 10^{-6}}$
$=\frac{1000}{320}=3.1\Omega$
$R=5\Omega$
$Z=\sqrt{R^2+{\left(X_L-X_C\right)}^2}=\sqrt{50}=7\Omega$
$tan\varphi =\frac{X_L-X_C}{R}$
$=1\varphi =45^{\circ }$