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Problem 38 Hard Difficulty

The capacitor in Figure $P 18.35$ is uncharged for $t<0 .$ If $\boldsymbol{E}=$ $9.00 \mathrm{V}, R=55.0 \Omega,$ and $C=2.00 \mu \mathrm{F}$ , use Kirchhoff's loop rule to find the current through the resistor at the times: (a) $t=0$ , when the switch is closed, and (b) $t=\tau,$ one time constant after the switch is closed.

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Video Transcript

I shown in this figure, it is Ah, CDs are C circuit and we need to find the current through the register while he's equal to zero. So that started the sip. A. We need to find Guidant to our when easy quitters you and the switch is closed. Like to start with this, since the values that already give it now the charge of the capacitor varies with time. So the question that we're going to use is Kyu is equal to capital Q multiplied by one minus us too. Minus D upon our C. It's marketed a question one, not this particular Q Bees, the maximum charge at equilibrium position. So this is known as maximum charge at equilibrium now. But you already know that Q is a product off capacities and the battery that is e M f. Okay, so in this C stands for capacitance, which is major in DMS off fats. And this is the GM if that is maximum world stage across capacity. No, What we need to do in the next step is we need to differentiate with respect her time. So we are going to write it down that is differentiating the aggression one with respect to time and what we get is all right down take you upon DD they Did he offer dd off the interrogation that is Q multiplied by one minus years to minus t upon our C no lettuce substitute See multiplied by e for Q and Deke You by Dee Dee Floor I that its current because current is the rate of change off charge with inspector time. You know, in the next beach I write it. Therefore, I easy going to d by Dickie off in place off you were reading see multiplied by my compared by one minus Edith's to minus D upon our C Now that it's all this further Dixie out and in the bracket now D by Dede off one minus ears too minus D upon our c No, it is a different shoot. Let's see, with the specter one, it is gonna be Zito. And with respect to David E off serious Twix is, except to eat is two ex again. So it is gonna be minus one upon our C multiplied by minus off idiots to minus g appointing a C. Therefore, let's stick see inside. So c'mon prepared by e upon our sea with minus site multiplied by minus years too minus D upon our C minus sign gets cancelled ultimately becomes plus, Therefore, I easy quit too e upon our multiplied by ears to minus t upon our city. This is the final question that we get now we have three values. The values are which had already given easy quick Tonight word our is equal to 55 homes and C is equal to two microphones that substitute these values in about immigration. Therefore, I z equal to nine forced upon 55 homes and greediness to minus Steve becomes you because that is equal to zero. We need to find out upon our C. So our committee, it is gonna be nine warred upon 55 homes and that becomes one because we're right. The reason it is 20 is equal to one. So begin the value as 0.163 amperes. So this is the final answer for the step, eh? Now let's move the state beef. We need to find the current to the register. So we need to find the value off I at he is in Quarter Tao Tao is RC time constant? So we need to find current at physical to Tao. That is one time constant. I write down one time constant after the switch is closed. So we're going to make use of the same equation here. So therefore all right down Isaac quite do e upon our into Edie's to minus t upon our see this aggression which we have derived. So now let's for the values. But before that we do even right RC as though And you would be esto therefore e upon our indoor. It is to minors we substitute toe upon r C is equal to two hours. Well, so again we'll put the town here which is equal to he upon our into ears too. It is going to be minus one right down. The reason If you want your latest always equate to RC No which is equal. Do let's put the values that is easy called a knighthood and our is equal do 50 firearms and it is to minus one become 0.367 So therefore we're right here. The current through the register is equal to 0.601 ampere it's what it didn't bracket, which is the answer. So now we're right. The final answer, as thus gardened two. But this jer that he is equal to town when the suit is closed is 0.601 appear and this will be our pride and answer for the step be.

Top Physics 102 Electricity and Magnetism Educators
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