Alternating Current

JEE Main level, numerical answer, medium

83 of 190

Question 83 of 190

An inductor of inductance 2μH2\mu H is connected in series with a resistance, a variable capacitor and an AC source of frequency 7kHz7kHz. The value of capacitance for which maximum current is drawn into the circuit is 1xF\dfrac{1}{x}F, where the value of xx is ______.
(Take π=227\pi =\dfrac{22}{7})

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Answer: 3872

For maximum current in series LCR circuit,
XC=XL⇒12πfC=2πfL{X}_{C}={X}_{L} \Rightarrow \dfrac{1}{2\pi fC}=2\pi fL
⇒C=14π2f2L=14×π2×49×106×2×10−6\Rightarrow C=\dfrac{1}{4{\pi }^{2}{f}^{2}L} =\dfrac{1}{4\times {\pi }^{2}\times 49\times {10}^{6}\times 2\times {10}^{-6}}
⇒C=13872F\Rightarrow C=\dfrac{1}{3872}F
Therefore, x=3872x=3872.

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