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Consider the circuit below. (a) What is the initial current through resistor $R_{2}$ when the switch is closed? (b) What is the current through resistor $R_{2}$ when the capacitor is fully charged, long after the switch is closed? (c) What happens if the switch is opened after it has been closed for some time? (d) If the switch has been closed for a time period long enough for the capacitor to become fully charged, and then the switch is opened, how long before the current through resistor $R_{1}$ reaches half of its initial value?

So here after the first switch has been closed a long time. We have We have a current I equaling 250 volts divided by 500 arms. And this is going to be equal 2.500 abs now. Ah, when asked, one is open when this first which is opened and the second switch is closed. This means that a current decay R L circuit is produced and this is all from the diagram. All from the diagram is of the circuit s So we can say that Let's get a new workbook and say that the function of current current as a function of time is going to be equal to ah initial times e x p e to the negative resist negative negative resistance multiplied by time, divided by the induct in CE s O here we know that for part A, I not the initial Mmm Ah, current is going to be equal to the max current. So this would be 0.500 out gramps for part way. We want to find the time constant, So Tower time constant is going to be ableto induct in CE divided by the resistance. So this would be 300 times 10 to the negative third Henry's and then divided by 500 arms. And this is giving us 6.0 times 10 to the negative forthe second. So this would be our time constant. And then for part C, we know that when time reaches infinity, this becomes extremely, extremely small, which means that I is equaling Sarah amp so as T reaches as t As time goes on, the current is decreasing more and more and more because again, this is a current decay. So as time goes on, the current goes down and again, as T approaches infinity, I will approach zero amps. That is the end of the solution. Thank you for watching.

In this problem, we have to calculate the time at which current will decrease toe, half of which initial value. So we need to calculate the small T unless spoken by writing the equation for the current at any time. T as eyes equals two. I not here is far minus are divided by l small t hear this. I noticed the currently at time T equals to zero are it is the maximum current are is the resistance cell is the indignance on the street? Is that time now we can whiter the equation for the small t as multi is equals to minus LD worded by our A little off I do wanted by I don't So this will be our equation about one. Now, in order to calculate the resistance in terms off investments, we need to apply the records rule Thio because working toe the Cuban circuit so we can right here I r plus l d. I divided by DT is equals to zero. So by inserting well, listen to this question. We can right here 12.0 on pair into our plus, uh, into here we can write minus 36.0 a pair per second is equal to zero. So from here, we can white value for this our as our is equals to 36.0 appeared per second into L Divide by 12.0 pair. All this came before the written as our is equals to 3.0 per second into help we can white equate Number one is it's Maltese equals two minus l rewarded by 3.0 per second into L. Ellen off I, which is equals to 6.0 impaired divide by 12.0 pair. So from here we can write the value for the small ts Maltese equals two 0.23 seconds. So this is the answer to this problem. Thank you.

Questions. What's your and wow common that goes sign with So it's not It's very don't know about physics behind the gun. Uh, inside the circus, determine the current I, Which this equation is you German such current. And the exit now. Hey, any time of yours under the determine how much current and is going inside. Okay, time in one second. So and the question you can know that I iz entrance off time So time is here variable in which I is dependent on so other finds out how much the kind 40 equals It's just simple By talking once once again relation with t exist. So here and here the other team. So I Oh, little 0.1 for all foreign, eh? Exponential thing Sign Dan like. And the answer is approximate the zero point for nine nine Right now keep in mind. And using the calculator, you have to convert they on the correct answer. If you use degree, you would get another, uh, number here, which is all right. So make sure that your calculator radium. Now that's more saying procedure applies here. Just luck ended with lies. And in this place Yeah, So then would I? They have one flies that can equal Sam for me now, eh, Linus? Three must have dogged by 4.5 sign then has supplied by on this. Oh minus opened then one.

Not to find Yossi Constant. For this question, we all need to finding effective resistance first and to find out your new simply file security a bit. So first off, you knew. Fine. We at r one and r tree together because the i n c V sweep each other. So this is 40 kills. They re at this armor plus artery. We've are too, which is in parallel with each other. So we have the rest vocals. So one of the 10 cubes pass 1/40 close in Versed gets it killed. It's all final, uh, resistance for the parallel portion. And then we are in ce Suif are for So we were at the overall equivalent resistance will be it secure. Blast articulo homes. So this study kilograms and now we can't find the RC Constant, which justic 38,000. What, like by 100 Michael Milly Ferrets. This will give us tree Is your zero seconds next to find the initial current in these circuits, we're gonna assume that we are looking at the current. That is ah, actually running truly battery. All right? And to find out, we all need to use the overall resistance and the overall Petrie Yemen. My sister batteries are collected. Siri's So the MF in total is just 24 plus 24 just 48 foods. So the current just e m f d followed by the equivalent resistance just 48 followed by 3000 jerky. 1st 1.26 I'm sent to a po minus tree. Ah, MPs Now to find what's the time require before the current regis half its initial current. So the current and given point time is, of course, the initial currents I not which is over here my proper exponential to eat negative t over r C. It is the exponential decay off currents in an RC circuit. We want I to be half off the initial current, so that means everyone I to be I not over to, Right? So now we can't cancel the I not in both sides of the equation get just half closed toe exponential off negative. T o r c be taken along on both sides and every multiplier negative R c over to d left hand side to our t if 26 34 seconds