A sinusoidal voltage V(t) = 200sin 2000t volt is applied to a series LCR circuit in which L = 10 mH, C = 25 and R = 100 Ω. The impedance of the circuit is _______ Ω Numerical answer type. Work it out, then open the answer.

Answer: 100. ω = 2000 rad/s XL = 2000 × 10×10⁻³ = 20 Ω XC = 12000 × 25×10⁻⁶ = 20 Ω XL = XC, so Z = R = 100 Ω.

A sinusoidal voltage V(t) = 200sin 2000t volt is applied to a series… | JEE Main 2022 (30 Jul, Shift 2)

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Series LCR Circuit

A sinusoidal voltage $V(t) = 200\sin 2000t$ volt is applied to a series LCR circuit in which $L = 10\text{ mH},\ C = 25\ \mu\text{F}$ and $R = 100\ \Omega$ . The impedance of the circuit is _______ $\Omega$

Numerical answer type. Work it out, then open the answer.

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Answer: 100

$\omega = 2000\text{ rad/s}$
$X_L = 2000 \times 10\times10^{-3} = 20\ \Omega$
$X_C = \dfrac{1}{2000 \times 25\times10^{-6}} = 20\ \Omega$
$X_L = X_C$ , so $Z = R = 100\ \Omega$ .

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