All Problems

Electric Oscillations

Problem 4.119

A circuit consisting of a capacitor with capacitance \(C\) and a resistance \(R\) connected in series was connected at the moment \(t=0\) to a source of ac voltage \(V=V_{m} \cos \omega t .\) Find the current in the circuit as a function of time \(t\).

Reveal Answer
I=VmR2+1/(ωC)2[cos⁡(ωt−φ)−cos⁡φ⋅e−t/RC],tan⁡φ=−1omegaRCI=\frac{V_{m}}{\sqrt{R^{2}+1 /(\omega C)^{2}}}\left[\cos (\omega t-\varphi)-\cos \varphi \cdot \mathrm{e}^{-t / R C}\right], \quad \tan \varphi=-\frac{1}{omega R C}
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