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

Answer 1

The correct option is A $7\Omega$ and ${45}^o$

$X_C=\frac{1}{\omega c}=3.125\Omega$

$X_L=\omega c=8\Omega$

$R=5\Omega$

Total impedance =$\sqrt{R^2+{(X_C-X_L)}^2}$

=$\sqrt{5^2+{(8-3.125)}^2}$

$\approx 7\Omega$

$\tan \varphi =\frac{X_C-X_L}{R}$

$\Rightarrow \varphi \simeq {\tan }^{-1}\left(1\right)$

$\Rightarrow \varphi ={45}^0$