Alternating Current

JEE Main level, numerical answer, medium

23 of 190

Question 23 of 190

An inductor of 0.5mH0.5mH, a capacitor of 200μF200\mu F and a resistor of 2Ω2\Omega are connected in series with a 220V220V ac source. If the current is in phase with the emf, the frequency of ac source will be ______×102Hz\times {10}^{2}Hz.

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Answer: 5

Given here: L=0.5×10−3HL=0.5\times {10}^{-3}H
C=200×10−6FC=200\times {10}^{-6}F
R=2ΩR=2\Omega.
If current is in phase with emf, so this is the condition of resonance.
f=fR=12πLC=12×3.14LCf={f}_{R}=\dfrac{1}{2\pi \sqrt{LC}}=\dfrac{1}{2\times 3.14\sqrt{LC}}
f=16.280.5×10−3×200×10−6=503.55Hz=5.03×102Hzf=\dfrac{1}{6.28\sqrt{0.5\times {10}^{-3}\times 200\times {10}^{-6}}}=503.55Hz=5.03\times {10}^{2}Hz

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