Q147 / 180 · COMEDK 2023 (Memory Based) · Physics

In the series $L-C-R$ circuit shown, the impedance is Figure

  • A
    $200 \Omega$
  • B
    $100 \Omega$
  • C
    $300 \Omega$
  • Correct answer
    D
    $500 \Omega$

Solution

Here, $L=1 \mathrm{H}, C=20 \mu \mathrm{F}, R=300 \Omega$ $\begin{aligned} & X_L=2 \pi f L=2 \pi\left(\frac{50}{\pi}\right) \times 1=100 \Omega \\ & X_C=\frac{1}{2 \pi f C}=\frac{1}{2 \pi\left(\frac{50}{\pi}\right) 20 \times 10^{-6}}=500 \Omega \end{aligned}$ Impedance, $\begin{aligned} Z & =\sqrt{R^2+\left(X_C-X_L\right)^2} \\ & =\sqrt{(300)^2+(400)^2}=500 \Omega\end{aligned}$

Hence, the correct answer is option: 'D'.

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