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Problem 68 Hard Difficulty

A 2.00 -nF capacitor with an initial charge of 5.10$\mu \mathrm{C}$ is discharged through a $1.30-\mathrm{k} \Omega$ resistor. (a) Calculate the magnitude of the current in the resistor 9.00$\mu s$ after the resistor is connected across the terminals of the capacitor. (b) What charge remains on the capacitor after 8.00$\mu \mathrm{s} ?(\mathrm{c})$ What is the maximum current in the resistor?

Answer

a.
b. q=0.235 \mu c
c. 1 \cdot 96 \mathrm{A}

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Video Transcript

in order to calculate the magnitude of the current in nine microseconds in this particular sum. Now let's make use off this to formula. So I just write down the to formally that we are going to make use off in this particular problem. The 1st 1 use Q is Equality Captain Q. Because the initial charge multiplied by eat is to minus t upon our C. I just mentioned you had this is called Lazar Any sure charge? And let's mark this as equation one. The second question already the formula that you're going to use his eyes equal to G Q upon DT. Now it is basically the aggression to with Steve that it is a read of change are charged with respect to time that is current. So when we start with the step A to find the magnitude of the current in nine microseconds. So this is work we need to find out nine microseconds. So let's start with this. No, First we'll put the value off I. Any questions do in the question What? So therefore, what we get here is Isaac quickly d by geeking off que multiplied by eat is to minus t upon our C. This is what we have. Solving this further taking Daddy, where do we get It's minus one upon our C Because everybody of readers to x x and duties twigs so minus one upon RC multiplayer back you as constant which has been taken out and eat us to X That is easiest to minus D a policy. This is the value of I rather the question that we're going to make you. So now just shut down the data which is given here for the city. Your keys. He could do nine, including Mr minus six seconds. Value off the capacitor is to Nanna Fa so to include Ennis to minus nine friends value far as 1.3, including this 23 homes. Thank you as 5.10 include candidates to minus six columns. Now we go to the next page in order to do this calculation. So we need to find I discovered and in nine microseconds which will mention as like us is equal to mind this one upon going to see monkey died like you into eat astute minus t upon RC. Now let's put the value is very carefully here. So minus one of all, all right, down 1.3 in pretenders to three homes multiplied by the value of the capacitor as doing too generous to minus nine. Multiplied by Q. The value of Q is 5.1 in group and is to my six clumps multiplied by it is to no minus D upon our see Surtees nine micro second. So nine interventions to minus six again audible remains seem That is 1.3 in glutinous 23 monkey blood by value of the capacitor asked, You know no for the moving ahead, but just write it as 5.1 in drunkenness to minus six. But negative sign upon 1.3 into tenderness to three Mikey part about doing good candidates to minus nine and value off it is to minus t upon our sea. In the calculator, we're getting it as 0.3138 So, for the calculation gives its value at 0.615 amperes, which I can write does 61 0.5 million beers. So this is bored. We get the value for gardened in nine microseconds. Next, mark this with an answer and final in a scepter manner began. Right? He does. We're right here. Does what you're in descending that magnitude off. The current in this case becomes 61.5 million on beer, and this will be I'll find an answer for the city. Now that's more. Let's try to get the answer for step. Be hundreds. We need to find the remaining charge in the capacity so we'll assume let the remaining judge on the capacity after eight microsecond be Q eight micro sicky. So now, therefore Q. Each micro seeking Did you charge after eight microsecond is equal to We're going to make use of this formula that is charged in to eat is to minus t upon our C, which is equal to charges given us 5.1 micro to 5.1 interventions to minus six multiplied by Here's to minus D so minus off aid to my group. Well, you are is 1.3 into tennis to three. Mikey played by while you have see is giving us to Nano. So going to Dennis to minus nine. That's calculated this eaters to ex term. So we write 5.1 indigenous to minus six and multiplied by 0.461 to get the value as 2.35 on one into Canada's two minus seven columns. So which could be taken as 0.235 include Ennis to minus six. Colom's So this is the answer, which we can write in a descriptive form again so we can write it. As thus the remaining charge on capacity is 0.2 35 into candidates to minus six. Williams. This is what we can right here. It's market as final answer. No, we go to the next page to get dancer for step. See, in this we need to find a maximum garland in the register. So just write down. We need to find maximum current and register. Okay. Now we need to understand one thing that the current all right down the current through a register is maximum. During discharging of the capacitor judging golf capacitor, we need to always remember that it dix always minimum time to discharge, break the value of the country, be maximum. So therefore, I'm Max is equal to one upon our embassy marquee players like you, Mike applied by ears to minus T upon our C. So which is equal to when upon value of registered is 1.3 in pretenders to three homes, Many of the capacities to nano multiplied by Q as 5.1 in pretenders to minus six columns multiplied by eaters, too. Minus t upon us in our here will mention the time as ineligible or minimum so we can mention it at zero and went right down the value of our as 1.3 indigenous to three and to include senators to minus nine. So now it is 20 upon something that means eat extra zero. So you used to zero is one. So we can just have the combination off 5.1 indigenous to minus six upon 1.3 in too generous to three into to include entities to minus nine, which is coming as finally one point 961 on beers. So just write down to find an answer for this. So this maximum current is 1.961 on beers. This is what you get nation as final answer

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