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Electric Oscillations

Problem 4.124

A series circuit consisting of a capacitor with capacitance C=22μFC=22 \mu \mathrm{F} and a coil with active resistance R=20ΩR=20 \Omega and inductance L=0.35HL=0.35 \mathrm{H} is connected to a source of alternating voltage with amplitude Vm=180 VV_{m}=180 \mathrm{~V} and frequency ω=314 s−1\omega=314 \mathrm{~s}^{-1}. Find: (a) the current amplitude in the circuit; (b) the phase difference between the current and the external voltage; (c) the amplitudes of voltage across the capacitor and the coil.

Reveal Answer
4.124. (a) Im=Vm/R2+(ωL−1/ωC)2=4.5 A;I_{m}=V_{m} / \sqrt{R^{2}+(\omega L-1 / \omega C)^{2}}=4.5 \mathrm{~A} ; (b) tan⁡φ=\tan \varphi= =ωL−1/ωCR,φ=−60∘=\frac{\omega L-1 / \omega C}{R}, \varphi=-60^{\circ} (the current is ahead of the voltage); (c) VC=Im/ωC=0.65kV,VL=ImVR2+ω2L2‾=0.50kVV_{C}=I_{m} / \omega C=0.65 \mathrm{kV}, V_{L}=I_{m} V \overline{R^{2}+\omega^{2} L^{2}}=0.50 \mathrm{kV}
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