Hey guys. In this video, we're going to talk about phasers and how they apply to the voltages and currents through inductors. Alright, let's get to it. Remember guys, that there are 2 functions that are very important regarding inductors in AC circuits. The current through an inductor and the voltage across an inductor at any time t. These functions are ωt, and the voltage occurs at some different angle θ′, which is ωt+π2. Because both functions occur at different angles, they are said to be out of phase. Okay? The current actually lags the voltage in this case, or you could say the voltage leads the current. What this means is readily apparent in phaser diagrams. In the first diagram, I plot the current at its angle ωt. In the second diagram, I plot the voltage at its angle ωt+π2, plus that 90 degrees. Combining these 2, we have the voltage ahead of the current by 90 degrees. Alright? It's very, very important to remember that the voltage across an inductor leads the current. This is opposite to capacitors in AC circuits, where the voltage lags the current. They're opposites. The voltage leads the current for inductors. The voltage lags the current for capacitors. Let's do a quick example about this. An AC source is connected to an inductor. At a particular instant in time, the current in the circuit is negative and increasing in magnitude. Draw the phasers for the voltage and the current that correspond to this instant in time. So here's my phaser diagram. Remember, what does it take for a phaser to be negative? It has to be on the left side of the graph because its horizontal component has to be negative. What does it take for it to be increasing in magnitude? It has to be moving towards the horizontal axis. Since it rotates counterclockwise, it has to be in the second quadrant. This has to be here so that it's negative, and since it's rotating counterclockwise, it's moving towards the horizontal axis. This is for the current. Remember that the current through an inductor lags the voltage. If you look all the way above in the green box, the voltage leads the current by 90 degrees. So, I would need to draw another phaser 90 degrees ahead, and that would be the voltage across the inductor. This is our phaser diagram for an inductor in an AC circuit. Alright, guys, this wraps up our discussion on phasors and how they pertain to inductors in AC circuits. Thanks for watching.
31. Alternating Current
Phasors for Inductors
31. Alternating Current
Phasors for Inductors - Video Tutorials & Practice Problems
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concept
Phasors for Inductors
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Video transcript
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Problem
ProblemAn AC source operates at a maximum voltage of 75 V and is connected to a 0.4 H inductor. If the current across the inductor is i(t) = iMAX cos[(450 s −1)t],
a) What is iMAX?
b) Draw the phasors for voltage across the inductor and current in the circuit at t = 4.2 ms. Assume that the current phasor begins at 0°.
A
a) imax = 0.42A b) θiL = 108o θVL = 198o
B
a) imax = 0.42A b) θiL = 108o θVL = 18o
C
a) imax = 0.42A b) θiL = 198o θVL = 108o
D
a) imax = 0.42A b) θiL = 18o θVL = 108o