Phase angle:

$\overline{){\mathbf{tan}}{\mathbf{}}{\mathbf{\varphi}}{\mathbf{=}}\frac{{\mathbf{X}}_{\mathbf{L}}\mathbf{-}{\mathbf{X}}_{\mathbf{C}}}{\mathbf{R}}}$

$\begin{array}{rcl}{\mathbf{\varphi}}& \mathbf{=}& {{\mathbf{tan}}}^{\mathbf{-}\mathbf{1}}\frac{{\mathbf{X}}_{\mathbf{L}}\mathbf{-}{\mathbf{X}}_{\mathbf{C}}}{\mathbf{R}}\\ & \mathbf{=}& {{\mathbf{tan}}}^{\mathbf{-}\mathbf{1}}\frac{{\mathbf{(}}{\mathbf{737}}{\mathbf{\times}}{\mathbf{112}}{\mathbf{.}}{\mathbf{5}}{\mathbf{\times}}{{\mathbf{10}}}^{\mathbf{-}\mathbf{3}}{\mathbf{-}}\frac{\mathbf{1}}{\mathbf{737}\mathbf{\times}\mathbf{11}\mathbf{.}\mathbf{6}\mathbf{\times}{\mathbf{10}}^{\mathbf{-}\mathbf{6}}}{\mathbf{)}}}{\mathbf{83}}\end{array}$

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 φ, the phase angle between the generator voltage and the current in this circuit. The phase φ is defined to be positive if the current leads the generator voltage, and negative otherwise.

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