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Concept #1: Phasors for Inductors


Hey guys, in this video we're going to talk about phasors and how they apply to the voltages in the currents through inductors. Alright, let's get to it. Remember guys that there are two 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 just given here and remember that they both occur at a different angle. The current occurs at an angle of omega T and the voltage occurs at some different angle theta prime which is omega T plus Pi over 2. Because both functions occur at different angles, they are said to be out of phase. The current actually lags the voltage in this case or you could say the voltage leads the current and what this means is readily apparent on phasor diagrams. In the first diagram I plot the current at its angle omega T. In the second diagram I plot the voltage at its angle omega T plus Pi over 2, plus that 90 degrees. Combining these two, we have the voltage ahead of the current by 90 degrees. 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 of 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 phasors for the voltage and the current that correspond to this instant in time. So here is my phasor diagram, remember what does it take for a phasor 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 counter-clockwise 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 so it's negative and increasing in magnitude. This is for the current. Remember that the current across, sorry, the current through an inductor lags the voltage. If you look at all the above in the green box, the voltage leads the current by 90 degrees so I would need to draw another phasor 90 degrees ahead and that would be the voltage across the inductor and that is our phasor 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.

Practice: An 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°.