An inductance of 2 mH , a condenser of $20 \mu \mathrm{~F}$ and a resistance of $50 \Omega$ are connected in…

An inductance of 2 mH , a condenser of $20 \mu \mathrm{~F}$ and a resistance of $50 \Omega$ are connected in series to an a.c. source. The reactance of inductor and condenser are same. The reactance of either of them will be
  1. $100 \Omega$
  2. $50 \Omega$
  3. $40 \Omega$
  4. $10 \Omega$

Solution

$\begin{aligned} & \text { Given } \\ & \omega \mathrm{L}=\frac{1}{\omega \mathrm{C}} \\ & \therefore \quad \omega^2=\frac{1}{\mathrm{LC}} \\ & \omega=\frac{1}{\sqrt{2 \times 10^{-3} \times 20 \times 10^{-6}}}=5 \times 10^3 \\ & \mathrm{X}_{\mathrm{L}}=\omega \mathrm{L} \\ & =5 \times 10^3 \times 2 \times 10^{-3} \\ & =10 \Omega \end{aligned}$ .

Asked in: MHT CET 2024 (16 May Shift 2)

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