For the series LCR circuit shown in the figure what is the resonance frequency and the amplitude of

Question

For the series LCR circuit shown in the figure what is the resonance frequency and the amplitude of the current at the resonating frequency?\

Professor PC Thomas Classes · Answer

Resonance angular frequency\ $\omega_{0}=\frac{1}{\sqrt{\mathrm{LC}}}=\frac{1}{\sqrt{8 	imes 10^{-3} 	imes 20 	imes 10^{-6}}}$\ $\omega_{0}=\frac{10^{4}}{\sqrt{16}}=\frac{100}{4} 	imes 10^{2}=2500 \mathrm{rad} / \mathrm{s}$\ $\mathrm{I}=\sqrt{\left(\frac{\mathrm{V}}{\mathrm{R}}ight)^{2}+\left(\omega \mathrm{CV}-\frac{\mathrm{V}}{\omega \mathrm{L}}ight)^{2}}$\ $\mathrm{I}^{2}=\left(\frac{220}{44}ight)^{2}+\left(25 	imes 10^{2} 	imes 20 	imes 10^{-6} 	imes 220-\frac{220}{25 	imes 10^{2} 	imes 8 	imes 10^{-3}}ight)$\ $\mathrm{I}^{2}=(5)^{2}+(11-11)^{2}$ or, $\mathrm{I}=\sqrt{5^{2}}=5 \mathrm{~A}$\