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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 |
$10Ω$ and $\tan^{-1}\left(\frac{5}{3}\right)$ 7Ω and 45° $10Ω$ and $\tan^{-1}\left(\frac{8}{3}\right)$ $7Ω$ and $\tan^{-1}\left(\frac{5}{3}\right)$ |
7Ω and 45° |
$ 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 $ $\text{Total Impedance } Z = \sqrt {R^2+(X_L - X_C)^2} = 5\sqrt 2 \Omega = 7\Omega$ $\text{Phase Difference } = tan^{-1}\frac{X}{R} = 45^o$ |
