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6) The electric current (in A)in a certain cnuit 25 function of time (in s) i5 i =5+6t. What total charge Passes. point in the cinuit in7 $2 329 € B) 152 â...

Question

6) The electric current (in A)in a certain cnuit 25 function of time (in s) i5 i =5+6t. What total charge Passes. point in the cinuit in7 $2 329 € B) 152 € C)47€ D) 182 €7) A certain capacitor is measured to have roltage of 82 JCOS- At this instant a (urrentas a function of tine given by 0.03Mis sent through the circuit After second, the voltage is measured to be 92 V What is the capacitance? A) 200 * 10-5 B) 2.00 *10-} 200 * 10-2 F D) 6.00 * 10-4 F8) You are driving Jlong highway ata s

6) The electric current (in A)in a certain cnuit 25 function of time (in s) i5 i =5+6t. What total charge Passes. point in the cinuit in7 $2 329 € B) 152 € C)47€ D) 182 € 7) A certain capacitor is measured to have roltage of 82 JCOS- At this instant a (urrentas a function of tine given by 0.03Mis sent through the circuit After second, the voltage is measured to be 92 V What is the capacitance? A) 200 * 10-5 B) 2.00 *10-} 200 * 10-2 F D) 6.00 * 10-4 F 8) You are driving Jlong highway ata steady 83 ft / sec when you see deer ahead and slam on the brakes What constant deceleration i5 required t0 stop your car in 291 ft? 23.67 ft /se2 B) 0.08 ft/s? 5.92 ft/52 D) 1L.S4 ft/se 2



Answers

A $2.0-\mu \mathrm{F}$ capacitor is charged through a $30-\mathrm{M} \Omega$ resistor by a 45 $\mathrm{V}$ battery. Find $(a)$ the charge on the capacitor and $(b)$ the current through the resistor, both determined $83 \mathrm{~s}$ after the charging process starts. The time constant of the circuit is $R C=60 \mathrm{~s}$. Also, $$ q_{\infty}=V_{\infty} C=(45 \mathrm{~V})\left(2.0 \times 10^{-6} \mathrm{~F}\right)=9.0 \times 10^{-6} \mathrm{C} $$ (a) $q=q_{\infty}\left(1-e^{-t / R C}\right)=\left(9.0 \times 10^{-5} \mathrm{C}\right)\left(1-e^{-83 / 60}\right)$ But $\quad e^{-83 / 60}=e^{-1.383}=0.25$ Then substitution gives $$ q=\left(9.0 \times 10^{-5} \mathrm{C}\right)(1-0.25)=67 \mu \mathrm{C} $$ (b) $i=i_{0} e^{-t / R C}=\left(\frac{45 \mathrm{~V}}{30 \times 10^{6} \Omega}\right)\left(e^{-1.383}\right)=0.38 \mu \mathrm{A}$

For this question. We're looking at a capacitor being attached Siri's three resistor in an air missiles. So it's quite a simple set up. We are given all of devalue us Such s T E m f the resistance throw ste contestants or your find is you're power dissipated by our resistance the energy being stored Bioko, Bester and also the power dissipated by the source right tree, different points in time. So the first point in time will be just when the circuit is formed. Night equals zero. When the current just started to fool the mature is 20 is a ghost in finite. So after a very long time and finally ET the point in time is when the church, close to half of its final value gonna start off. If the 1st 1 one MTI close to zero just started. Ah, just out of anti circuit. So the capacity can be ignored. Can assume that it's just a piece of wire. They're still charge. Start in it yet why needing? So we can just ignore and they're 40 power dissipated by oh, resistor. It's just Ah, using pique was to discover our you can take the entire um f off the battery to be the potential drop across the resistor. Give us 246 year old? No. For how much? Um, Sebesta is actually charging at the rip off church. We're gonna use the equation you request to que square, uh, to see and therefore you read off charging what ISS electrical energy is. Do you differentiating this? Ah, the only one that is depend on time is Cuba see so constant so you can keep net differentiating que que square yet to cure security? You know that security is just the current. So this is que times I see No, because that is nor church there is starting a capacitor yet so curious, Cyril. And the 40 Cent I thing is zero parts. We won't find a politician, bater by t source We just see to find what is the current flowing, truly anti circuit. You can find the Yemen power across the sauce by taking p crystal. I feel now the current you can find you think your sister taking the potential difference across the resistor and the resistance in this work for us Can't 246 year old what's now? We move on to the second point in time when t think was within finite. So after a very long time no, he the best er after a very long time will be fully charged. And now sn open circuit, right? No, allowing any current to flow and therefore there is no current and without any current, the powerful the resistor which is a p goes to I square are oi fi pique was civil because it depends on I and also the potential trouble cause it eu sou west Bill course this No, I de still current flowing through it The power I already read off Great off accumulation off the energy in the capacitor since it is dependent or que So you better cue and I if I think zero this entire thing will be to really the power dispute about the sauce is also zero because there's no current for the third point. Really? When did you start effect that are cure? It's no half off you're not. We used to equation you Not one minus absolute sorry exponential negative to you r c this sea equation to find out what is the charge at any point in time The secret is to are a specific point in time when we want que to be half off the maximum value you not We can rearrange Gary off the common factor and financial toe degree T o r c because to oh, now using this, we can actually find what is the current at our interested point time Since it is not times explanation negative t o I'll see. This will be just half off the makesem current and it makes my current of your reverse. The phone is this was 200. Any for five point it Using this current, we can find what it's d participated. Heidi zesa using P equals toe ice cream, huh? The ideas will give us 614. What for? The rich off charging Do you over tea t I know that, uh que right dirty q t t its current. I see we know what is the current but you know what? And you know I see charge is half t excellent church. Then we can find the next one charge based on curie goes toe cv. So this is the teachers I ve heavy is the potential of course Across uh, domestic This case, we can use the potential across our resistor. Yeah, we should need to find based on can use recently power potential costing investors just, um if subdirectory Yeah, this is going to be 120 for this is boats 60 four. Test will multiply this pretty current. Every should get Ah, 61 full 0.5. What? Finally he participated by t source? Yes, Stick I times. Um, if just this case 120 p 12 tree zero what's and I can see? Um, the power despite a power, um f is equivalent to the politics Peter body resistor last year, uh, reads off charging off our capacitor and so it it will be, ah, energy conservation.

Hi in this given problem the value of capacitor means capacities that is given us By 10 micro fatty and it is charged to our potential 20 kilovolt. First it is charged fully and then it is connected across a resistor. Having a resistance of 7.0 mega or to get discharged across it. Initial discharge current passing through this resistor will be given by i is equal to be by our simply using warm slaw things. This is 20 kg or 20,000 world divided by resistance 7.0 mega ohm or 7.0 into. And this bar six on. So this current here comes out to be 2.9 milli ampere. one of the answer for this given problem. Then we have to find time constant. We have to find the time to take in by the potential stalled potential raised over the plates of the capacitor To drop to 37% of its initial value. And we know going again what the voltage capacitor voltage to drop up to 37% of its initial value is known as time constant with a given c. Our circuit and that is given as the product of capacitance. With that resistance. So here Capacitance is 5.0 micro ferret means 5.0 into And its bottom -6 that it. And resistance is seven Mega home or 7.0 into And it's part six home. So finally this time constant here comes out to be 35 seconds which is another answer for the same given problem. Thank you

Hi there. So for this problem we have uh sets. Yeah point for nana Ferraris capacitor and it is being charged with potential difference of 24 bold use. Um And it is connected in Syria's with a coil that has um and in the tense of 0.0 60 sets and negligible resistance. So after the circus has been completed there are current oscillations of course, because of that independence. So part A of this problem is at what instant when the charge of the capacitor. So that problem. Now the charge of the capacity for this part is going to be 0.0. Aid me Crow cole arms. How much energy is the story in the capacitor and in the in doctor. And what is the current? Uh indian doctor? So we need to determine the um the energy indian doctor. They're going to call you of held and the current. So we know that initial energy store in the capacity or is chaired between the induct er and the capacitor. So the mutual energy in the capacity or is going to be used zero. We're gonna call it like that. one half of the capacities times the initial and potential difference. So we plot all of these values that we know 6.49 of our radios. Nano means 10 to the -9 for radios and 24 volt shoes square. So this will give us a value of 1.80 for micro jewels. This energy is chaired between the induct er and the capacitor. So the energy and the capacitor at this new time is going to be equal to the charge store on it over two times the capacities. So we will have that. We plot all those values. We know that the charge, the capacitor is 0.08 me crow Colom's Square over two times 6.40. None of our ideas. So when we plot this into the calculator, we obtain a value of seeds .5 micro jewels. So the energy remaining indian Doctor is just simply the The difference between the initial one and the energy is stored in the capacitor. So that will be 1.80 for micro jewels minus 0.5 mi cro jewels. The energy in the capacitor. So that will be 1.30 for me. Crow Ferrario. So this is the energy um in the in Doctor now and we know that the energy of the Doctor relates with the, With the current by the following four, of the in Dayton's times the current square. So we need to solve for the current this expression. So that will be two times them energy in the in the tour over the conductance and the square root of this. And this will give us the current. So okay of course we need to take the positive value because it is the physical interpretation. So that will be two times U. L. Over the independence. We plot dulls values in here. We know the value that we obtained for the energy which is 1.30 for um 34 times 10 to the minus sits because that's uh micro Over the importance which is 0.0 sits this sits so from this we're going to obtain that. The current indian doctor is 6.33. Yeah 37 times 10 to the minus three emperors. We can also convert this into a million pairs. That will be 6.37 milli amperes because merely is 10 to the minus three. So this is the current in the conductor. Now for party of this problem, we are told at the instance when the charge on the capacitor is the same as before. What are the voltages across the capacity and across the in doctor? And what is the rate at which current indian doctor is changing. So for this part we again have a 0.08 mi cro for areas um column. Sorry. And that's the charge in the capacitor. So when he took tane the potential difference when the capacity or charge is of this value and we found that the energy store in the capacitor is 0.5 mi cara jewels as we obtained before. So from there we can obtain the voltage, the new voltage in the in this capacity or so we will have to remember that this is related to one half of the capacities times the voltage in the capacity of the square. So if we solve for the politician, the capacitor is just simply two times you see oversee which is the capacities. So we plot all the information in here. So that's two times the energy story in there, which is 0.5 mi Cro jewels. That's the value that we obtained before. And with that charge of 0.08 Micro columns and the capacity is 0.40 Nana Farrah ideas. So we take the square root of all of this and we obtain about you for the potential difference of 12.5 bulges. So that's the potential difference in the capacity to read or now. The cross and the potential across the in that drawer. And the capacity tour is the same. So because they are in serious And so the potential of the capacitor is the same that the potential Indian doctors so that it is 12.5 bolts. Now, the next thing that we need to determine is how it's changing the potential and the electric potential in the in dot you are. So for that we used to follow in that the potential in the doctor is given by the um the magnitude of the independence times the variation of the current with respect to time. So we have That from here we can just sold for the variation of the current with respect to time. That's the value that we want to obtain. So that will be the potential difference in the in dr over the in Dayton. So that will be 12.5 balls over 0.0 60 sets. Which is the indulgence of this in doctor. So that will obtain that the um barry ation of the current in this in doctor is going to be 100 89 um Pers per second. So that's it for this problem.

Okay, so does Chapter 26. Problem 93. So it says an RC circuit contains a resistor are of 15 killer homes the the capacitor of 0.3 micro parents in a battery with an E m f nine volts. Starting a time equals zero when the battery is connected. Determined the charge Q on the capacitor in the current I and circuit from time equals t two. Time equals he time equals 02 time equals 10 milliseconds, and it wants to do it at 1.1 millisecond intervals for graphing capabilities. Cool, Cool made grass trimming the charge. Cute. I change with time. Um, from the grafts, find the time at which the charms. Okay, cool. So to figure out how in our C circuit you've always like this. We need to look back at the equations 26 6 a in 26 8 Okay, so what these show us is, they show us the charge as a function of time is given by C E. M f one minus B to the negative t over RC. They also show us the current as a function of time given as e M. F. Over our E to the minus t over RC. Okay, now, from this, we can immediately graft these with graphic capabilities. It's about the second part First for a second. So it says, find the time at which the charge of chains 63% of its final value. So if we want the charge to be 0.63 que final. Okay, well, what is Q Final? Just a question to final for charge. You can see as t goes to infinity. This approaches to this c times t m f. So this is 0.63 C times. Now we can display visit time 0.3 micro thirds times line votes That comes up to being 1.7 times 10 to the negative six schools. Mrs R. Q. I'm gonna call it P for an appointment. Find them a graph. Let's do the same thing for current. So I p is now. We wanted to be 37% of the final. Great. Well, again, the final current is given. Oh, sorry. As the initial current final charge with the initial Kurt, the initial current is given by looking at this time equals zero just absolutely over our. So this town become 0.37 slung over our 0.37 nine votes over 15 killer homes. And we get an I P. Of 2.22 times 10 to the negative for wimps. So these are the two points we want to figure out on our cards and current versus time plants. So from these equations are we have to do is get an array of T. If you want to use this and pipeline, you can do some pie dot lynn space 0 to 10. No seconds at a point. One nanosecond in between. This gives you an array, and then you can just evaluate this at each point and then plant it. So I'm gonna go ahead and sketch what the parts are gonna look like here. So it's straw this charge versus time slot. So this is time in seconds. 0 to 10. Mrs. Charge, uh, zero, when I say appears to 0.5 racoons. So we started zero then. This kind of follows this kind of powder. Okay. And if we want to find the time when we just find when this equals R Q p that we found before and we should see that happens at about 4.4 milliseconds. Okay, let's plot the other wrong here. So this is the current Oh, sorry. This is still time on the X axis. Of course, this is time in milliseconds from 0 to 10 milliseconds. And now this is current. This goes from 0 to 0.6. This is Miller Imps. Now this We start at 06 kind, uh, decays very slowly along this path and again we should see that I p what we found before, the point that we wanted to find happens at the same time, which is roughly 4.4 no service.


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