Inductors in AC Circuits Video Lessons

Concept

# Problem: A 0.160 H inductor is connected in series with a 85.0 Ω resistor and ac source. The voltage across the inductor isvL = -(11.0V)sin[473 rad/s)t].Part A. Derive an expression for the voltage vR across the resistorExpress your answer in terms of variables L, R, VL (amplitude of the voltage across the inductor), ω, and t.Part B. What is vR at 2.04 ms?Express your answer with the appropriate units

###### FREE Expert Solution

Inductive reactance is expressed as:

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

Current passing through the resistor is:

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

But from the boxed equation, XL = ωL

Therefore,

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

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###### Problem Details

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

vL = -(11.0V)sin[473 rad/s)t].

Part A. Derive an expression for the voltage vR 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 vR at 2.04 ms?
Express your answer with the appropriate units