30. Induction and Inductance

LR Circuits

# Unknown Resistance in an LR Circuit

Patrick Ford

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Hey guys. So let's get to more practice with LR circuits we have in our circuit with the time constant and it's initially connected to a battery. And then, after some very, very small amount of time, it is disconnected from the battery, the current to something we're supposed to figure out what the resistance of the circuit is. So hopefully you guys realized that this word here it's disconnected from the battery means that we are working with decay. So we're working with current decay right here. So let's see. We have a time constant, which is tau. That's equal to 0.25 We have a voltage that's V is equal to 10 volts. We have time, which is equal to 0.5 seconds, and we have the currents at that specific times. That's I when t is equal to this value right here, and we're supposed to figure out what is the resistance of this circuit. So hopefully you guys realize that if we're working with current decay, then the equation that's gonna tie all of these things together is going to be the current decay equation. That's I of T is equal to V over r. And then do we have one minus sign there? No, because we just have the inverse exponential e to the minus t over Towel with one minus sign is for current growth. Because eventually what happens is we want that V over r to sort of be, like, away. You know, we want to be isolated, right? So this is the equation that is eventually going to go to zero as time gets really large. Got it? So here's what we have. We have the resistance of the circuit. That's gonna be our time. Our target variable right here. And let's see, we have the current as a function of time and we actually have what the current is at a specific value in times when t is a specific number. So all we have to dio is Let's see, I have I've t I know what the voltage is. I know what the time is. The time I'm plugging in is just this number right here. And I have the current at that specific time, and I have, with the time Constant is so. All I have to do is just move this over to the other side. So basically what happens is that just, like, sort of an algebraic equation? This Arkan go up to the top and this i of tea can actually go down to the bottom and basically just trade places with it. So that means that our is equal to V over I when t is equal 2.5 Um, And by the way, I'm just evaluating the current at the specific time. And then we have e to the minus t over towel. So let's plug in. All of our numbers are is equal to the voltage, which is 10 I at what, at this specific time is just equal to 0.5. Then we have e to the minus, and then T which is equal 2.5 and then we have over Tau and Tau is 0.25 Okay, so hopefully you guys plug this in. You could actually you know, you could take an extra step in, Sort of like, simplify this a little bit. 10 over 100.5 actually just becomes 20. And this exponential right here is actually e to the minus 0.2. And if you plug this into your calculator, you guys should get 16.4 and that's gonna be in homes. So that's the resistance off the circuit. Let me know if you guys have any questions.

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