# A sinusoidal voltage of peak value 283 V and angular frequency 320/s is applied to a series LCR circuit.  Given that R=5 , 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 : Option 1) Option 2)   Option 3) Option 4)

As we learnt in

Impedence -

$Z= \sqrt{R^{2}+\left ( \omega L -\frac{1}{\omega c}\right )^{2}}$

-

$V{_{0}} = 283 \ V$

R = $5\Omega$, L = 25 mH, C = 1000 $\mu$F

W = 320/s

$X_{L} = WL = (2\pi f) L = 320\times25\times 10^{-3}\Omega$

$8\Omega$

$X_{C} = \frac{1}{WC} = \frac{1}{320\times10^{-3}} \Omega = \frac{1}{0.32}\Omega$

$3.125\Omega$

Total Impedance

Z = $\sqrt{R^{2}+(X_{L}-X_{C})^{2}} \cong 5\sqrt{2}$

Phase difference = $tan^{-1} (\frac{X_{L}-X_{C}}{R})$

$\cong 45^{\circ}$

Option 1)

This is incorrect option.

Option 2)

This is correct option.

Option 3)

This is incorrect option.

Option 4)

This is incorrect option.

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