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 decreases.
Statement II: In a series LCR circuit, the value of power factor at resonance is one.
In the light of given statements, choose the most appropriate answer from the options given below.

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Statements I is correct but Statement II is false.

Statement I is incorrect but Statement II is true.

Both Statement I and Statement II are false.

Both Statement I and Statement II are true.

answer is D.

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Detailed Solution

In ac circuit, $I = \frac{V}{Z} = \frac{V}{\sqrt{R^{2} + {(X_{L} - X_{C})}^{2}}} = \frac{V}{\sqrt{R^{2} + {(ωL - \frac{1}{Cω})}^{2}}}$

As 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 decreases.

Power factor, $cosϕ = \frac{R}{Z} = \frac{R}{\sqrt{R^{2} + {(X_{L} - X_{C})}^{2}}}$

At resonance, $X_{L} = X_{C} \Rightarrow R = Z \Rightarrow cosϕ = 1$

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