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  4. In a series LCR circuit, the inductance, capacitance and resistance are L =100 mH , C =100 μ F and R =10 Ω respectively. They are connected to an AC source of voltage 220 V and frequency of 50 Hz. The approximate value of current in the circuit will be A.

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Q. In a series LCR circuit, the inductance, capacitance and resistance are $L =100\, mH , C =100 \, \mu F$ and $R =10\, \Omega$ respectively. They are connected to an $AC$ source of voltage $220\, V$ and frequency of $50 \, Hz$. The approximate value of current in the circuit will be ___$A$.Physics Question Image

JEE MainJEE Main 2022Alternating Current

Solution:

$X _{ L }=\omega L =2 \pi \times 50 \times 10^{-1}=10 \pi$
$X _{ X }=\frac{1}{\omega C }=\frac{1}{2 \pi \times 50} \times 10^{4}=\frac{100}{\pi}$
$R =10 \Omega$
$Z =\sqrt{\left(10 \pi-\frac{100}{\pi}\right)^{2}+10^{2}} \simeq 10 \Omega$
$i =\frac{ E }{2} \simeq \frac{220}{10} \simeq 22 \,Amp$