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7.Alternating Current
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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.....$A.$
A
$27$
B
$89$
C
$55$
D
$22$
(JEE MAIN-2022)
Solution
$X _{ L }=\omega L =2 \pi \times 50 \times 10^{-1}=10 \pi$
$X _{ X }=\frac{1}{\omega C }=\frac{1}{2 \pi \times 50} \times 10^{4}=\frac{100}{\pi}$
$R =10 \Omega$
$Z =\sqrt{\left(10 \pi-\frac{100}{\pi}\right)^{2}+10^{2}} \simeq 10 \Omega$
$i =\frac{ E }{2} \simeq \frac{220}{10} \simeq 22 Amp$
Standard 12
Physics
