JEE Mains · Physics · STD 12 -7. Alternating current

Given below are two statements: Statement \(I :\) Maximum power is dissipated in a circuit containing an inductor, a capacitor and a resistor connected in series with an \(AC\) source, when resonance occurs Statement \(II :\) Maximum power is dissipated in a circuit containing pure resistor due to zero phase difference between current and voltage. In the light of the above statements, choose the correct answer from the options given below :

A Statement \(I\) is false but Statement \(II\) is true
B Statement \(I\) is true but Statement \(II\) is false
C Both Statement \(I\) and Statement \(II\) are true
D Both Statement \(I\) and Statement \(II\) are false

Verified Solution

Answer & Solution

Correct Answer

(C) Both Statement \(I\) and Statement \(II\) are true

Step-by-step Solution

Detailed explanation

Power will be maximum when impedance is minimum \(Z =\left[ R ^2+\left( X _{ L }- X _{ C }\right)^2\right]^{\frac{1}{2}}\) At resonance, \(X _{ L }= X _{ C }\) \(Z_{\min }=R\)

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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