Alternating Current

JEE Main level, numerical answer, medium

101 of 190

Question 101 of 190

In a series LCR circuit, the inductance, capacitance and resistance are L=100mHL=100mH, C=100μFC=100\mu Fand R=10ΩR=10\Omega respectively. They are connected to an ACAC source of voltage 220V220V and frequency of 50Hz50Hz. The approximate value of current in the circuit will be _____ AA.

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Answer: 22

Angular frequency, ω=2πf=100πrads−1\omega =2\pi f=100\pi rad{s}^{-1}
Here, inductive reactance XL=ωL=(100π)(100×10−3)=10πΩ{X}_{L}=\omega L=\left(100\pi \right)\left(100\times {10}^{-3}\right)=10\pi \Omega
And capacitive reactanceXC=1ωC=1(100π)×(100×10−6)=100πΩ=10πΩ{X}_{C}=\dfrac{1}{\omega C}=\dfrac{1}{\left(100\pi \right)\times \left(100\times {10}^{-6}\right)}=\dfrac{100}{\pi }\Omega =10\pi \Omega
Now, impedance of the series circuit is Z=R2+(XL−XC)2=R=10ΩZ=\sqrt{{R}^{2}+{\left({X}_{L}-{X}_{C}\right)}^{2}}=R=10\Omega
Therefore,
IRMS=VRMSZ{I}_{RMS}=\dfrac{{V}_{RMS}}{Z},
=22010=22A=\dfrac{220}{10}=22A

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