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https://texercises.com/exercise/inductive-reactance/
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Exercise:
Show that the reactance and phase shift for an inductor coil are given by X_L omega L quad textand quad tanDeltaphi +fracpi

Solution:
For an inductor directly connected to a sinusoidal ac voltage it follows using the loop rule that vt + v_Lt V_ cosomega t - L fractextdittextdt With the general expression itI_ cosomega t - Deltaphi for the ac current we find V_ cosomega t -L I_ omega sinomega t - Deltaphi It follows that V_ L I_ omega labeleq and cosomega t -sinomega t-Deltaphi labeleq Using refeq we find the expression for the reactance: X_L fracV_I_ L omega Using the trigonometric identity cosomega t sinpi/ - omega t - sinomega t - pi/ and refeq we find that Deltaphi +fracpi
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Exercise:
Show that the reactance and phase shift for an inductor coil are given by X_L omega L quad textand quad tanDeltaphi +fracpi

Solution:
For an inductor directly connected to a sinusoidal ac voltage it follows using the loop rule that vt + v_Lt V_ cosomega t - L fractextdittextdt With the general expression itI_ cosomega t - Deltaphi for the ac current we find V_ cosomega t -L I_ omega sinomega t - Deltaphi It follows that V_ L I_ omega labeleq and cosomega t -sinomega t-Deltaphi labeleq Using refeq we find the expression for the reactance: X_L fracV_I_ L omega Using the trigonometric identity cosomega t sinpi/ - omega t - sinomega t - pi/ and refeq we find that Deltaphi +fracpi
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Electrodynamics
Tags
ac circuit, capacitor, reactance
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Difficulty
(3, default)
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Language
ENG (English)
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