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

Option: 1
22

Option: 2
-

Option: 3
-

Option: 4
-

Answers (1)

best_answer

$\mathrm{X_{L}=\omega L=(2 \pi f L)=100 \pi \times 10^{-1}} \\$

$\mathrm{X_{L}=10 \pi } \\$ ..........(1)

$\mathrm{X_{C}=\frac{1}{\omega c}=\frac{1}{2 \pi f C}=\frac{1}{100 \times 10^{-4}(\pi)}} \\$

$\mathrm{X_{C}=\frac{100}{\pi}} \\$ ............(2)

$\mathrm{R=10 \Omega}$

$\mathrm{Z =\sqrt{R^{2}+\left(X_{L}-X_{C}\right)^{2}}} \\$

$\mathrm{=\sqrt{100+\left(10 \pi-\frac{100}{\pi}\right)^{2}}} \\$

$\mathrm{ \simeq \sqrt{100} \simeq 10} \\$

$\mathrm{I_{\text {rms }} \frac{V_{\text {rms }}}{Z}=\frac{220}{10}=22 \mathrm{~A}}$

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