Current:

$\overline{){\mathit{i}}{\mathbf{=}}{{\mathit{i}}}_{{\mathbf{max}}}{\mathbf{cos}}{\mathbf{}}{\mathbf{\varphi}}}$

The voltage across the inductor:

$\begin{array}{rcl}{\mathbf{V}}_{\mathbf{L}}& \mathbf{=}& \mathbf{L}\frac{\mathbf{d}}{\mathbf{dt}}\mathbf{i}\\ \mathbf{0}& \mathbf{=}& \mathbf{L}\frac{\mathbf{d}}{\mathbf{dt}}{\mathbf{i}}_{\mathbf{max}}\mathbf{sin}\mathbf{(}\mathbf{\omega t}\mathbf{-}\mathbf{\varphi}\mathbf{)}\\ \mathbf{0}& \mathbf{=}& {\mathbf{Li}}_{\mathbf{max}}\mathbf{\omega}\mathbf{}\mathbf{cos}\mathbf{(}\mathbf{\omega t}\mathbf{-}\mathbf{\varphi}\mathbf{)}\\ \mathbf{0}& \mathbf{=}& \mathbf{cos}\mathbf{(}\mathbf{\omega t}\mathbf{-}\mathbf{\varphi}\mathbf{)}\\ {\mathbf{cos}}^{\mathbf{-}\mathbf{1}}\mathbf{0}& \mathbf{=}& \mathbf{\omega t}\mathbf{-}\mathbf{\varphi}\\ \mathbf{90}\mathbf{\xb0}& \mathbf{=}& \mathbf{\omega t}\mathbf{-}\mathbf{\varphi}\\ \frac{\mathbf{90}\mathbf{\xb0}\mathbf{+}\mathbf{\varphi}}{\mathbf{\omega}}& \mathbf{=}& \mathbf{t}\end{array}$

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 t_{1}, the first time after t = 0 when the voltage across the inductor is zero?

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