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Impedance of a Parallel LR AC Circuit

Patrick Ford
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Hey, guys, let's do an example using impedance. Okay. What's the impedance of a parallel l R circuit? Okay. L r a c circuit. Okay, so it has an induct er and a resistor in it. And let's draw the phaser diagram for this. When they're parallel when they're parallel, don't forget their voltage. Phasers are in phase because all elements in parallel have the same voltage. So I'm gonna draw some voltage phaser right here Now for the resistor, the current and voltage phasers air always going to be in phase. So here is the current fazer for the resistor. Now, the voltage phaser for the induct er is always going to lead its current fazer. So I need to draw the current phaser for the induct er as lagging by degrees. So here's the current fazer for the induct er. Now the maximum current in this circuit is going to be given by the vector sum of those two current phasers using Pythagorean theory. Um, I get this. Okay? Okay. Now I want to rewrite everything in terms of the maximum voltage. So this is V Max over the impedance. Remember, this is the definition of the impedance that the maximum current produced by the source is just the maximum voltage of the source divided by the impedance. This is gonna be the square root of V. Max squared over R squared, plus the max squared over X l squared. Why do both of these terms also have V Max? Because this is a parallel circuit. So everything has the same voltage as the source, right? So I can cancel all of these terms of V max. So this tells me that one over Z, the impedance is the square root of one over r squared. And I can substitute in the equation for the inductive reactant since, and this becomes one over omega squared elsewhere. And this is our impedance for a parallel L R circuit. For parallel circuits, you're never quite going to define the impedance. You're always going to find one over the impedance like this, but this is a perfectly fine way of representing the answer. All right, guys, Thanks for watching