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  4. In the given LCR AC circuit, the effective current (in ampere) flowing through the circuit is. <img class=img-fluid question-image alt=Question src=https://cdn.tardigrade.in/q/nta/p-r7vw58uvzie32yzo.jpg />

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Q. In the given $LCR$ $AC$ circuit, the effective current (in ampere) flowing through the circuit is.

Question

NTA AbhyasNTA Abhyas 2022

Solution:

$R=50\Omega$
$X_{L}=\omega L=50\Omega$
$X_{L}=\frac{1}{\omega C}=100\Omega$
$\Rightarrow Z=\sqrt{R^{2} + \left(X_{L} - X_{C}\right)^{2}}$
$Z=50\sqrt{2 }\Omega$
$I_{rms}=\frac{V_{rms}}{Z}=\frac{200 / \sqrt{2}}{50 \sqrt{2}}=2A$