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The voltage (in volts} across circuit given by Ohm' s Iaw: V = IR, where resistance Ri and Rz, parallel, then their combineo resistance given bYthe curent (in ...

Question

The voltage (in volts} across circuit given by Ohm' s Iaw: V = IR, where resistance Ri and Rz, parallel, then their combineo resistance given bYthe curent (in Jmps flowing through the circuit and R the resistance (in ohms). If we place two circuits withR-R+kSuppose the currentampsincreasino10- _ ampisec and Rq is ohms and increasing at 0.5 ohm/sec, while Rz is ohms and decreasing at 0, ohm/sec ,Calculate the ratewhich the voltage changingRound your ansuerthree declmal places:0.153Ratevolts{

The voltage (in volts} across circuit given by Ohm' s Iaw: V = IR, where resistance Ri and Rz, parallel, then their combineo resistance given bY the curent (in Jmps flowing through the circuit and R the resistance (in ohms). If we place two circuits with R-R+k Suppose the current amps increasino 10- _ ampisec and Rq is ohms and increasing at 0.5 ohm/sec, while Rz is ohms and decreasing at 0, ohm/sec , Calculate the rate which the voltage changing Round your ansuer three declmal places: 0.153 Rate volts{sec Josalute tolernce /-0.002



Answers

The voltage, $V$ (in volts), across a circuit is given by Ohm's law: $V=I R,$ where $I$ is the current (in amps) flowing through the circuit and $R$ is the resistance (in ohms). If we place two circuits, with resistance $R_{1}$ and $R_{2},$ in parallel, then their combined resistance, $R,$ is given by $$ \frac{1}{R}=\frac{1}{R_{1}}+\frac{1}{R_{2}} $$ Suppose the current is 2 amps and increasing at $10^{-2}$ amp/sec and $R_{1}$ is 3 ohms and increasing at 0.5 ohm/sec, while $R_{2}$ is 5 ohms and decreasing at 0.1 ohm/sec. Calculate the rate at which the voltage is changing.

So have at it. You know that the oldest is it related Current your eye for current. Their assistance. So, uh, so we know that our it's increasing, but to homeless person, you homes, it's sick. Um, the whole dish sells increasing, uh, three bolts second, then, uh, Holly's the guards. So you decide. Changing, uh, voltage Being able to boats, their receipts, those being equal to sports. He says he's measure four bombs. Oh, sauce you. I guess this is saying that these, uh, p r t that he said those are here. That is a theoretical the cold fish off the volume the politician with this 50 big time. So what we can do here is, uh, you can differentiate get a relation for it is Barabbas. So yeah, the fish Stan has to be ableto getting our quotient. So there's no question this with friendship. Oh, appreciating these this shit that there is one this. Use this plus Hi, James. Yeah, it did. So you have this equation? No. So you seem to have everything is here, But does he know Well, what they're asking here is what is the hiding? So these are But I want to find. What is that I'm being, You know, what is the assistance? You know, dear d you know that. You know, Did you see the rate of change in the whole dish? But you know what? We need to get this. It will. We're giving the coltish. So perhaps you can use this equation. So we know that build boats must be equal to current hands. Their assistance or almost So the the carriage, Your current, He's right there. You just divide by arms, So so helps. That is a current, but are currently people that are visible to three times for it's a poor goes away. Great. It was repeated. So we have a current of three builds. Um, so you have the bridge? Um, So you know these? Yeah. So the big city three bolts for a second must be equal to keep. I It do well, are there? See cities. Them's four arms for moms I'm dating now. Times off a bus. Uh, hi. Uh, three Bolt brown. Hold but home their issues. Lizzie's for arms. The deer here? Yeah, they were Great changes. Color season sees two. Your second. So our arms will we Wonderful So we have here these simplifies six. Well, you move that six bolts for second over there. So minus six nights worlds for second she will be. Oh, well, this is my most through These were here. That's minus three underworld. That will do the rate of change of food. Ah, current four arms. So well, you can just write, like, four rounds both sides, but for rooms, I'm second, so that, uh, well, he's, uh, goes away. So you have that Just get that are changing. The current was given by minus hit minus 3/4. Oh, my, uh, dynasty forts of Ah, voltage. Homesick. Uh oh. That's the units of he's just sick.

In this problem. We're circuit and were given that the will to that second circuit is 12 wolf. Any party ever has to find their Israel change. Insurance is expected, uh, resistance. So does a order. One resistance changes brain a 0.1 to 8 or 88. Um, so, firmness, we know that changing current using the also the slow or rape or inform my spoke. 08 So during final minus burn. So And we find this to be Nathan 01 you're 18 but And for me given Interval, we know that our teams from a 0.1 changing businesses point fun that people ovals In this in question, we find the average rate of change of current suspect thio business be negatives 0.0 when a fine right back for months. Or this is native ones on 9 to 5. The first bird Oh, the part. You were asked to find the change of terms respectfully uses those 80 um so we carry function for current S V over r there. Forget Liza Pilsen. So then my problem where there talk during the late to be o r sprint Now all we need to do this, but numbers in you find the I they are to be there. 12 you wanted but a spray. And this is nature. One negative. 0.187 If I ever. For every proxy, where has to find the right of changing resistance of spectra current members So the are over the eye eyes walking by again We're gonna have all the same procedure our zebra Rubio, hon Don't forget the end that he's accustomed. So are most people are going to be late to be spreading that. Let's just, uh, get numbers in well, this week on the orderly to be next 12 squared and that is ICO to about negative 51 33 home for four.

Either. When this problem we're giving were given the following information we're giving alms law, but the equals I are, and plus these for other bits of information. So the only thing we'll have to tie them all together is, uh, using this formula and looking at the derivative of both sides. So if we I think Oh, the derivative of you with respect to tea now we're given that right. But the important part is we can get the right side a little easier. All right, so we know how to calculate DVD t. Since V is a function of I and are we could just use the chain rule and the change Will says that DVD T must also equal partial of the with respect to i times d i g plus partial of e with respect to our time tr tt. And at this point, we have almost every I think everything we need to plug in the DVD t I was given to us. That's a negativo 0.1 Uh, good partial of the with respect to huh? I we can calculate, of course, by looking just at this formula here. So partial of v with respect to I please consider I to be the variable than that derivative is just are okay d i d t So that's what we're asked to find So we wouldn't expect to know that yet Partial on V with respect to our again, we'll look at our formula here of the equals i r and this time the derivative respect our is just I and finally d r d t we are given that one. That's 10.3 so negative 0.1 equals were also given the current values of our and I. So now we have everything we need Ours 400 time d I t t I is the 0.8 times three. All right. And and see So our final value of the I t t will move this term that's attracting it from both sides. So you have a 0.1 minus. I see no 0.8 times open three and then want to divide all that by 400 and that will give us our value of D I d t. Um So just plug this into a calculator now and we will get negative zero points. Did you get all the zeros here. Uh, see 0000 three one. And our units, we can look back at, ah, given information. But since I was given an amps, that will be your unit. And our time unit in this problem is all seconds. So their their final answer for how I is changing. Hopefully that helped.

Uh huh. The voltage V across the resistance are generates a current unit amps. I. Is equal to be over our. We want to answer when our is five homes and it's increasing at .2 homes for a second. What is the rate of change of the current for V is equal to 9V. So this question is testing our understanding of rates and related rates. Namely it's testing our ability to apply the derivative for problem solving purposes so we can go ahead and solve first. Let's note that we're assuming B is constant. So the rate of change is I respect the time is D I E. T. Is equal to D. D. T. V over R. Or negative view over R squared er DT because V remember does not change the time. So it's a constant. So now that we have D I. D. T, we can simply plug in R. B. R. And D R D. T. So I'm saying G I D T equals negative 9/5 square 10.2. Or of the final solution. The idea is equal to negative 0.72 amps per second.


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