$\mathrm{L}=2 \mathrm{H}, \mathrm{C}=5 \mathrm{mF}$ and $\mathrm{R}=12 \Omega$ are connected in series to an…

$\mathrm{L}=2 \mathrm{H}, \mathrm{C}=5 \mathrm{mF}$ and $\mathrm{R}=12 \Omega$ are connected in series to an a.c. generator of frequency 50 Hz . Then
  1. at resonance, impedance of the circuit is zero.
  2. at resonance, impedance of the circuit is $12 \Omega$.
  3. the resonant frequency of the circuit is $1 / 2 \pi$.
  4. the inductive reactance is less than the capacitive reactance.

Solution

Impedance, $\mathrm{Z}=\sqrt{\mathrm{R}^2+\left(\mathrm{X}_{\mathrm{L}}-\mathrm{X}_{\mathrm{C}}\right)^2}$ At resonance $\begin{array}{ll} & \mathrm{X}_{\mathrm{L}}=\mathrm{X}_{\mathrm{C}} \\ \therefore \quad & \mathrm{Z}=\mathrm{R} \\ \therefore \quad & \mathrm{Z}=12 \Omega \end{array}$

Asked in: MHT CET 2024 (02 May Shift 2)

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