Given below are two statements: Statement I: When the frequency of an a.c. source in a series LCR circuit increases, the

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Given below are two statements: Statement I: When the frequency of an a.c. source in a series LCR circuit increases, the current in the circuit first increases, attains a maximum value and then…

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Given: Two statements about a series LCR circuit.

Find: Which option correctly identifies the truth values of Statement I and Statement II.

In a series LCR circuit, as the frequency of the a.c. source increases, the impedance changes with frequency. The current therefore first increases, becomes maximum at resonance, and then decreases beyond resonance. So Statement I is correct.

At resonance in a series LCR circuit, the inductive reactance and capacitive reactance become equal, so the circuit behaves as purely resistive. Hence current and voltage are in phase, and the power factor becomes $1$ . So Statement II is correct.

Therefore, both Statement I and Statement II are true. The correct option is D.

Note: The solution labels the correct option as A, but its explanation clearly concludes that both statements are true, which matches option D in the given options.

Given: A series LCR circuit and two statements regarding current variation with frequency and power factor at resonance.

Find: The correct option.

For a series LCR circuit, current is given by

I = \frac{V}{Z}

where impedance is

Z = \sqrt{R^2 + (X_L - X_C)^2}

As frequency changes, $X_L$ and $X_C$ change, so impedance decreases up to resonance and then increases again. Therefore current rises first, is maximum at resonance, and then falls. Hence Statement I is true.

At resonance,

X_L = X_C

so

Z = R

which is minimum for the series circuit. Then the phase angle is $0$ , so power factor is

\cos \phi = 1

Hence Statement II is true.

Therefore, the correct option is D.

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