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(10 points) Find the differential equation, in terms of the charge Q that mnodels series circuit that has capacitor of C=3 farad, an inductor of L=2 henry, and resi...

Question

(10 points) Find the differential equation, in terms of the charge Q that mnodels series circuit that has capacitor of C=3 farad, an inductor of L=2 henry, and resistor of R=3 ohms_ JUST SET UP THE DE Is the system overdamped? Why why not?

(10 points) Find the differential equation, in terms of the charge Q that mnodels series circuit that has capacitor of C=3 farad, an inductor of L=2 henry, and resistor of R=3 ohms_ JUST SET UP THE DE Is the system overdamped? Why why not?



Answers

Use the differential equation for electric circuits given by
$L \frac{d I}{d t}+R I=E$
In this equation, $I$ is the current, $R$ is the resistance, $L$ is the inductance, and $E$ is the electromotive force (voltage).
Solve the differential equation for the current given a constant voltage $E_{0} .$

Hello. The question is taken from differential equation where we need to solve this differential equation. And the question is did you, where did he less? one of our our scene to you is equal to E by our the RNC are constant and the value of you. That is the initial condition. Who is equal to zero B. Is equal to zero. Now we know that how one can solve it that has evaluate the integrated factor that is equal to U. To the power integration. One by us seeing two DT. That is equal to U. To the power T by I'll see. Let us multiply this integrated factor to our vacation. We get into the power T over RC. Take you over dating plus into the poverty over RC divided by R. C. Into that is able to eat by our each of the power T over I'll see into the poverty or are these just a question. So that equation we can try to test the over duty to eat to the poverty over I'll see is equal to over our U. To the power to your taking this DDT town to the right hand side. We get day off you into the power P by R C. Is equal to a by R. E. To the power by RC into duty integrating both sides. And eventually we get you into the power T by L. C. Is equal to E. By our into the power T by RC. Into a city where will begins allowed plus case that the constraint of integration. So we get who is equal to taking it to be poverty by us. To the right hand side. We get E E C plus K to the power dynasty by RC. And the boundary condition is that these equal to zero. U. is equal to zero. So we get okay is equal to minus E. In to see which is the required value of this constraint. So after substituting this value, you will be equal to easy into one minus E. To the power minus B. Bye. Okay, which is not required value for discharge. Hope this clears your doubt and thank you.

You got our sister 400 to the naked eye. So we got the equipment. Six Double. 400 for you. Divided by who? He's here. 10 86 clones. Q prime. You get 0.6 r squared was for our team. For people here. I make it 100,000 plus four Squared three. Yeah, you e he, uh I just want out us keys. Where que zero. You? You wait three Each native, one of my three minus 50 square of 3 70 one thing 1003 Really? You prime Fear will be too. I see one. It's good. We have a post 50 off minus 50 square. See you. Rain is 1000 way, I think. Here So see equal 27 5 20 plus square CTO train sitting into the equation But above you B b c two people to town naked six We're fight to times square above three entering C two into one equations fee One of many people tend to ladies naked Problem plus square Did you take the square root to the city? In the next six? Making 20 was square 37 to square with 3 70 e to the negative off, maybe 100 g plus And in the anchor six. That case we're ready 20 plus where three deputy multiplied by each and negative off each 1000. He was put minus 1000 years e to the negative one. I eat too negative. 1000 1000 plus post 50 square Ruutel 3 70 Divide a bit theory.

You have a nen dr of zero Point Henry's resistor 200 homes capacitor, uh, 10 to the negative for Tintin. Negative. Negative for So you have to the equation. Simply be zero point for a huge double prime plus 200 few prime cause 10,000 cute tear que zero. He's going cool. Q Prime of zero is equal to zero, which is which is included her second, which is the current which is AM's by rearranging at your gate que double time close five. Fine. You time. 25,000 Hughes called Europe All right there plus 500 r plus 95,000 people's You know, our would be equal Teoh blankets to 50 score. Hey, T square root Uh, did you you He would be able to see one year to you Where? Seek your ear to 15 square here que zero b c one plus two contentedly in 85. Teoh uh, see one, maybe square. You need to 50 square The king us Teoh Mais to negative 2 50 Because square uh, 15 q prime here would be see one rolled by. He's where c t multiple Nice to waas 50 square between. If you want people to Nice by Square teen By five course, where t c two I entered into the great urgency to be equal. Teoh I plus Square 15 kids Where. Profit. 10 Negative five, Which is people Teoh three plus square by 600,000 See one people to Mainz five plus square. 15 teams were 15 10 negative five. Just equal Cube three. Nice. Where by 5 600,000 So then Q of t then the main square 600 multiply by he make it it to square E plus three Poor square 56 here E e e square off e This just since 50 times where you mean multiplied by.


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