Inductive reactance is expressed as:

$\overline{){{\mathbf{X}}}_{{\mathbf{L}}}{\mathbf{=}}{\mathbf{\omega}}{\mathbf{L}}}$

Current passing through the resistor is:

$\mathit{i}\mathbf{=}\frac{\mathbf{V}}{{\mathbf{X}}_{\mathbf{L}}}$

But from the boxed equation, X_{L} = ωL

Therefore,

$\overline{){\mathbf{i}}{\mathbf{=}}\frac{\mathbf{V}}{\mathbf{\omega}\mathbf{L}}}$

A 0.160 H inductor is connected in series with a 85.0 Ω resistor and ac source. The voltage across the inductor is

v_{L} = -(11.0V)sin[473 rad/s)t].

Part A. Derive an expression for the voltage v_{R} across the resistor

Express your answer in terms of variables L, R, VL (amplitude of the voltage across the inductor), ω, and t.

Part B. What is v_{R} at 2.04 ms?

Express your answer with the appropriate units

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