Secpe ?0 P044oleLla To420 mH inductor; an 9.0 $2 resistor; and a 12.0 V battery are connected in series_ The switch is closed at t = 0 Find the voltage drop across ...

A $25-\mathrm{mH}$ inductor, an $8,0-\Omega$ resistor, and a $6.0-\mathrm{V}$ battery are connected in series. The switch is closed at $t=0$. Find the voltage drop across the resistor (a) at $t=0$ and (b) after one time constant has passed. Also, find the voltage drop across the inductor (c) at $t=0$ and $(\mathrm{d})$ after one time constant has elapsed.

For part A were asked to find the voltage drop across the resistor. At T equals zero seconds. And after one time, constant has passed. Okay, well, the voltage across the resistor, we'll call it Visa Bar is equal to the potential supplied by the battery up salud times one minus E to the minus t, which is the amount of time divided by the time constant towel. So when t is equal to zero, this is equal to the battery times one minus e to the zero E to the zero is equal the ones This is at the battery times one minus one, which is equal to zero weaken box I dent is their solution for a for part B were asked to find the potential across the resistor when the time that has passed is equal to one time constant. So this is gonna be absolute times would might this e to the minus towel over Tao, which is e to the minus one. So carrying out this expression, we find that B is equal to 3.8 volts. Weekend box. It is the solution for question. Be question C asked us to find the potential across the induct er will call that Visa Bell. This is equal to absolute minus I r. So using Kirchoff ce rule, this is equal to the battery minus potential across the resistor which is equal to playing in the value for the potential across three sister of the battery minus herbal supplied by one minus E to the minus t over towel. This comes out to equal absolutely tyrants e to the minus t over towel. Well, for part C were asked to consider when t is equal to zero. So this is equal to Absalon, which is equal to the six Volt. So it's just the potential the battery become box. It is their solution for seat and finally party. We're gonna use the same equation we just found for the potential across the induct er times e to the minus. Well, this is t over towel, but this is when tea is equal. That house, this is minus Would this comes out to equal 2.2 bolts weaken box and it is your solution

Yeah. In discussion and party we are going to calculate the E. M. F. Of the battery. But first to calculate the P. M. We need to calculate the maximum got it. So we use the question of maximum current in the circuit to calculate the I. M. F. Of to. That's great. So the maximum coming in the circuit is the ratio of the IMF of the battery. And the distance that is imax is equal to. He divided by our or we can say up silent divided by not here. Silence is the E. M. F. Of the battery and art. Is that the distance in that circuit? Now as we need to calculate E. M. So we rearrange the situation for Absolutely it is Absalon is equal to Imex multiply by are now we substitute eight mp here or Imex and 0.30 home for uh in the about equation. Therefore we get E M. F. Is equal to 2.4 water. Therefore I am of of the batteries. 2.4 world now comes to party. So here we need to calculate the independence of the circuit. So for this views like creation for time on stand in a northern circuit, it can be written as T equal to L divided by arts. Now here L is a independence and R is the resistance. Now we rearrange the situation for L therefore and is equal to three multiplied by our no obstruct you. 0.25 2nd 40 and 0.30 On. for us we get and equal to 75 million Henry. Therefore the independence of the circuit 75 million Andriy no comes to part C. So here we are going to calculate the equation for current in the circuit after one time on stand elapsed. So for this we use the expression for change in current in RL circuit after time interval Dalby. It can be didn't as I equal to Imex multiply by one minus each of the powers minus small thing divided by capital. He now here actually capital T. Is time constraint. Imex is initial current. I is finally current and he is dying. So at time T equal capita G. The elbow equation changes. Has I equal Imex multiply by one minus E. To the power minus one. No, we can write this as I equal imax 1 0 three 67 As each of the power -1 is equal to zero 367 Therefore get I is equal to I mix Multiplied by zero 63 two. Now here we substitute eight M. Pierre for Imex in equation and Sold for current in the circuit after one time constant elapsed therefore I is equal to eight, multiplied by 0.63. You So after multiplication We get I equals two five blind one and beer Therefore the question for current and the circuit after one time constant collapsed is 5.1 ampere No. In party we are going to calculate the voltage close the register after one time constant has elapsed and later we will find the voltage drop Close the conductor also. So was for mortgage echoes arrested after one time for state has elapsed. We write the expression for potential difference across the register which is equal to the product of the resistance. Anger getting that can be written as shelter. We are is equal to minus. I know many people who are now here negative sign shows that induced potentially presidency opposing direction to that change in that. Got it. No, We substitute five points one M. Pierre for I and 0.30 all or us. Therefore we got Then we are is equal to -1 five world. No, you're fine Walters rob across conductor. We apply your jobs. No rules to the circuit. So the summer world is law across the component is equal to zero. That is silent plus delta V. L. Yes Than we are is equal to zero. Now we rearrange this equation for there'll be hell. Therefore there really is equal to minus absolute minus that. We odd. Now Subsequute 2.4 World for a silent and -1.5 world for that'll be us. In the equation we get Dell. We L is equal to minus two point or world -1.5 war. Therefore we got then we and is Well to -0.90 voice. Therefore the bolt is rope across the indicator is -0.90 World

Hello students in this question we have an conductor of inductive liquids to 400 million Henry. That is equal to 0.4 Henry. And the resistance. R. One equals two homes and R two equals two homes are connected with the battery of E. M. F. We not is equal to 12 old as sure the intern orations of the battery is negligible. That is zero. Okay so at the equals to zero time the switch as he is closed. Okay so we have to determine the potential drop across the induct er So from the circuit we can find that the world is across our one will remain always be known because it is in parallel with it. Okay and walt is across the conductor will decay will decay with respect to the time. Okay because it is connected in series with the resistance are so V. L. Is given by the note it with the power minus T. They were by now. Okay so how is equals two L. By our So this is equal to L. Which is zero and four. The whereby our which will be here are too so that is equal to the food. Okay Okay now this is equal to 0.2 seconds. Now we can substitute the values in this situation so we will obtain from here that we L. Is equal to be not. That is 12 old into the power minus city where they now that is a 0.2 second. So after solving the voltage across the conductor will be equal to six P. To the power minus five G. World. Okay, This movie is unit, so this become answer of the problem. Okay? So from the given options, Option D. Is correct. Okay uh Option C. Is the correct answer. Uh this is 12 here. six. Okay, this will you? Okay? Thank you.

All right. So for part a, uh, we're going to use the fact that, um it reaches half its maximum current in 0.1 seconds so I over my max will be half. This ratio is actually absolute absolute of our PMF of resistance times one minus this exponential factor, the time constant in it over the max, which is just enough over are So those things cancel like you're left with. Um, so you have 1/2 is equal to to one minus exporter of dynasty. Roberto. So, uh, you can take, um Won't have to the right hand side expert Exponential term to the left hand side. What you get is exponents physical to 1/2. Take the log of that. And so TV will be negative. Tao o r. Um heard me, uh, Tao, uh, will be if negative TV over log of quite five and negative t is they just 0.1 seconds over larger point and that is divided by a lot of 0.5. Gives you a time constant of point 144 seconds. All right. Uh, part B, um, in part B, we're just using homes law. So enough across the conductor is I r current times resistance and appoint 15 seconds. I is half of too. So that's one NPR and Resistance is four and five homes. This gives you 4.5 volts. Ah, and in part, see same homes a lot. But this time met after the switch of clothes. So this is two amps. That's its maximum current times. Uh, the same resistance. So this gives you nine volts.