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Consider the circuit shown in the sketch. The battery voltage is80.0 V. R1 = 20.0 ohms, R2 = 40.0 ohms, and L = 0.500 H. Initiallythe switch is open and no currents...

Question

Consider the circuit shown in the sketch. The battery voltage is80.0 V. R1 = 20.0 ohms, R2 = 40.0 ohms, and L = 0.500 H. Initiallythe switch is open and no currents are flowing. What is the voltageacross the inductor immediately after the switch is closed?zero20.0 V40.0 V80.0 V160.0 Vnone of these answers

Consider the circuit shown in the sketch. The battery voltage is 80.0 V. R1 = 20.0 ohms, R2 = 40.0 ohms, and L = 0.500 H. Initially the switch is open and no currents are flowing. What is the voltage across the inductor immediately after the switch is closed? zero 20.0 V 40.0 V 80.0 V 160.0 V none of these answers



Answers

In the circuit shown in Figure $21.64,$ the battery and the inductor have no appreciable internal resistance and there is no current in the circuit. After the switch is closed, find the readings of the ammeter $(A)$ and voltmeters $\left(V_{1}$ and $V_{2}\right)$ (a) the instant after the switch is closed; (b) after the switch has been closed for a very long time. (c) Which answers in parts (a) and (b) would change if the inductance were 24.0 $\mathrm{mH}$ instead?

In the first part of this problem, we're going to find the readings off meter and water meter, then stand off to the switch is closed. So we need to calculate uh then we have to kill that we won on. We have to write the value for the two eso when I equals Tau zero impair. At that case, we one will be equals Tau zero world. Now we can write we one plus we two is equals toe 25 points there worked. So this could be further written as zero plus we two is equals toe 25.0. So from here we can write to be too is equals toe 25.0 world and a major will give us the value is equals to zero a pair In part b of this problem we're going to find the readings off a meter and water meter. After a long time that switch is closed so we need to calculate And then we have to write the video for we won Onda value for me too After the long time That is when he goes to infinity we too will be equals Tau zero World and we can white we want Plus we two is equals to I am and we know they tell this we want Plus, we two is equals to 25.0 world So from here we can write it we want plus zero is equals to 25.0 world So we can write To be one is equals toe 25.0 What? And from here we can write this we want Plus you is equals to ir So from here we can write the value for I as icicles to we want divided by our by inserting what is into this question? We can write icicles to we want which is equals to 25.0 world divided by which is close to 15 point zero mega. So from here we can write the Baylor for I has icicles to 1.67 and pad so the meter will read is equals to 1.67 impaired Since the above answers do not depend upon the indignance. Therefore the agreement Sam and off the question Thank you

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

So off to switch. EJ s is closed and at some later time we have given that de i ut the rate of change of kind. Is he looking 50 MPs per second? So we have the rate of change of kind Indians calculate the potential difference across points see and deep, which is across the in doctor and this but in traditions. Is he going to out time to the I get to and these values and no So we can calculate this to be zero for three Henry's times change of current but 50 MPs per second answer gets put into a difference to be 15 boats. Now we can apply, have you proof? And so with Cuspide approved with the new at the top So the top U tells us that 60 bulls easy put two. I won times are one and hence we can calculate this current I want recently 60 bullets divided by our Owen which is given as fucked Bones. It's just kind. I won is equal to one boy fire MPs. Now we apply a new poll again, this time to the bottom You. This one can be expanded as follows so 60 volts minus I to are to minus of Gene Bolles. Because actually both is equal. Does you know opinions Use the new print again and resolved I to So I to is equal to 60 goals. We simplify over 25. Those are two in the end, Forget kind of I to to be equal to one, 48 and ps. So now we have I want and I to. But after a very long time is past I to is equal to 60 bowls divided by Actually, this is about 60. This that's for you. Funny. 60 minutes 15 45. But after a long time, this is 60 goals divided my existence, 25 homes, which gives us in different kinds. Like to that's too point for and piers and community with this which is open the in doctor maintains this coat. It's at that point I won is the same as I to just to full MPs. So come into our one changes abruptly when this which is closed

So if we apply catch ups loop rule here we see that we get the phone in question. So excellent minus y times are minus l a times d I d t which is equal to zero. And from here we can figure out the folded across the resistor. Let's call it a V A B and that's gonna be Epsilon minus l a times d i d t So this I r wanted your idea is people that across the resistor. So now if we use the given numbers, we see that absolutely has given us 18 holes minus l is 0.38 Hendry and the I d. T is basically 7.2 ampere per second. So combining this we get 15 pointy folds. So that's the boulders across the resistor. Thanks for watching


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