**Concept:** Phasors for Resistors

Hey guys, in this video we want to talk about phasors specifically applied to resistors in AC circuits, Alright let's get to it. Remember guys that the voltage and the current across a resistor at any time T is given by these two equations these two functions right here. They are both at the same angle omega T, remember that angle for any phasor is omega T because both of these functions both of these cosines have that same angle they are said to be in phase, in phase means identical I'll show you what this means in the context of the phasors drawn below. The first phaser that I drew is the current through the resistor and it is at some angle omega T. Next I drew the voltage across the resistor which is at that same angle omega T. So when I combine these phasors into a single phasor diagram. I get that the current and the voltage across the resistor line up because they are both at this angle omega T they are said to be in phase they line up any two phasors that are in phase will always be lined up as they rotate so at anytime that you choose to measure it will always be lined up sorry they will always be lined up.

This is the conclusion that we're going to take away from this video that the voltage across the resistor is in phase with the current through the resistor it's very important to remember that now it's do a quick example. An AC source with an angular frequency of 20 inverse seconds is connected to a resistor with the circuit broken 0.2 seconds after the circuit is completed draw the voltage phasor and the current phasor when the circuits broken nothing is happening the second it's closed now time starts. So the question is if we want to draw those phasers what is that angle that they're going to be at? That angle for the phasors always going to be omega T. So this is going to be omega which we were told is 20 inverse seconds times T which we're told is 0.2 seconds. So this is going to be 4 radians which is equivalent to 229 degrees if you just convert quickly between radiance and degrees so now we know how to draw our phasors.

229 degrees places us in the third quadrant because that's greater than 180 and last then 270 so thats going to put us somewhere around here 229 degrees. We're going to have a phasor for the current Oh sorry guys a little technical difficulty a phasor for the current and we're also going to have a phasor for the voltage sorry if those colors are the opposite of what I before the color itself doesn't really matter and these are in phase and you can draw other angles if you want like this angle or this angle it doesn't really matter as long as whatever angle you choose it matches up with this angle of 229. Alright guys thanks for watching this video that wraps up our talk about phasors with respect to resistors and AC circuits alright.

**Problem:** A 12 Ω resistor is connected to an AC source. If the resistor’s voltage phasor is initially at 0° , and the figure below shows the phasor after 0.04 s, answer the following:

a) What is the angular frequency of the source? Assume the phasor is on its first rotation.

b) What does the current phasor diagram look like?

c) What is the current in the circuit at this point (t = 0.04 𝑠)?

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