φ_{C} = 90° - 22.3 = 67.7°

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

A circuit is constructed with an AC generator, a resistor, capacitor and inductor as shown. The generator voltage varies in time as ε =V_{a} - V_{b} = ε_{m}sinωt, where ε_{m} = 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 V_{C} = V_{d} - V_{a}, the voltage across the capacitor, at time t = 0? Note that V_{C} is a signed number.

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