Alternating Current

JEE Main level, single correct, medium

76 of 190

Question 76 of 190

Given below are two statements:
Statement I : When the frequency of an AC 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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Answer: (C) Both Statement I and Statement II are true

When an a.c. voltage is applied in a series LCR circuit, the current is increased first, attains a maximum and then decreases.
The formula to calculate the power factor is given by
cos⁡ϕ=RR2+(XL2−XC2)...(1)\cos \phi =\dfrac{R}{\sqrt{{R}^{2}+\left({{X}_{L}}^{2}-{{X}_{C}}^{2}\right)}}...\left(1\right)
At resonance, XL=XC{X}_{L}={X}_{C}, Hence,
cos⁡ϕresonance=1\cos {\phi }_{resonance}=1
Thus, both the statements are true.

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