A sinusoidal voltage of peak value 283 V and angular frequency 320/s is applied to a series LCR circuit. Given that $R=5Ω, L=25 mH$ and $C=1000 μF$. The total impedance, and phase difference between the voltage across the source and the current will respectively be
Answer & explanation
Correct answer: option 2
$ R = 5\Omega$
$\text{Capacitive Reactance} X_C = \frac{1}{\omega C} = \frac{1}{ 320\times 10^{-3}} = 3\Omega$
$\text{Inductive Reactance} X_L = \omega L = 320\times 0.025 = 8\Omega$
$\text{Total Reactance } X = X_L - X_C = 5\Omega $
$\text{Total Impedance } Z = \sqrt {R^2+(X_L - X_C)^2} = 5\sqrt 2 \Omega = 7\Omega$
$\text{Phase Difference } = tan^{-1}\frac{X}{R} = 45^o$