MHT CET · Physics · Alternating Current

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

A \(100 \Omega\)
B \(50 \Omega\)
C \(40 \Omega\)
D \(10 \Omega\)

Verified Solution

Answer & Solution

Correct Answer

(D) \(10 \Omega\)

Step-by-step Solution

Detailed explanation

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

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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