JEE Mains · Physics · STD 12 -Alternating current
- JEE Mains 2022
- Hard
- MCQ
For a series \(LCR\) circuit, \(I\) vs \(\omega\) curve is shown \((A)\) To the left of \(\omega_{r}\), the circuit is mainly capacitive. \((B)\) To the left of \(\omega_{r}\), the circuit is mainly inductive. \((C)\) At \(\omega_{r}\), impedance of the circuit is equal to the resistance of the circuit. \((D)\) At \(\omega_{t}\), impedance of the circuit is \(0\). Choose the most appropriate answer from the options given below
Pick an option to check your answer.
Answer & Solution
Correct Answer
(C) \((a)\) and \((c)\) only
Step-by-step Solution
Detailed explanation
\(\text { at } \omega_{r}, X_{C}=X_{L}\)
\(\Rightarrow \frac{1}{\omega_{r} C}=\omega_{r} L\)
So if \(\omega < \omega_{r}\) then \(X_{C}\) will increase and \(X_{L}\) will decrease.
Hence to left of \(\omega_{t}\) circuit is capacitive
\(Z=\sqrt{R^{2}+\left(X_{C}-X_{L}\right)^{2}}\)
at \(\omega_{r}, Z =\sqrt{ R ^{2}+ O ^{2}}= R ( C )\)
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