A series LCR circuit consist of $R = 80 Ω, X_{L} = 100 Ω and X_{C} = 40 Ω$ . The input voltage is 2500 cos (100 $π$ t) V. The amplitude of current, in the circuit is ____A

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answer is 25.

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Detailed Solution

$V_{0} = 2500 volt, w = 100 π$
$\begin{array}{l} z = \sqrt{{(X_{2} - X_{2})}^{2} + R^{2}} = \sqrt{(100 - 40)^{2} + 80^{2}} = \sqrt{60^{2} + 80^{2}} = 100 \\ I_{0} = \frac{V_{0}}{2} = \frac{2500}{100} = 25 \end{array}$

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