Series LRC Circuits Video Lessons

Concept

# Problem: A circuit is constructed with an AC generator, a resistor, capacitor and inductor as shown. The generator voltage varies in time as ε =Va - Vb = εmsinωt, where εm = 120 V and ω = 737 radians/second. The values for the remaining circuit components are: R = 83 Ω, L = 112.5 mH, and C = 11.6μF.What is VC = Vd - Va, the voltage across the capacitor, at time t = 0? Note that VC is a signed number.

###### FREE Expert Solution

φC = 90° - 22.3 = 67.7°

$\begin{array}{rcl}{\mathbf{V}}_{\mathbf{C}}& \mathbf{=}& \mathbf{i}{\mathbf{X}}_{\mathbf{C}}\\ & \mathbf{=}& \frac{\mathbf{i}}{\mathbf{\omega }\mathbf{C}}\mathbf{s}\mathbf{i}\mathbf{n}\mathbf{\left(}\mathbf{\omega }\mathbf{t}\mathbf{-}{\mathbf{\varphi }}_{\mathbf{C}}\mathbf{\right)}\end{array}$

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###### Problem Details

A circuit is constructed with an AC generator, a resistor, capacitor and inductor as shown. The generator voltage varies in time as ε =Va - Vb = εmsinωt, where εm = 120 V and ω = 737 radians/second. The values for the remaining circuit components are: R = 83 Ω, L = 112.5 mH, and C = 11.6μF.

What is VC = Vd - Va, the voltage across the capacitor, at time t = 0? Note that VC is a signed number.