solve-the-given-problems-the-current-i-in-a-in-an-amplifier-circuit-as-a-function-of-the-time-t-in-s

Question

Solve the given problems.
The current $i$ (in $A$ ) in an amplifier circuit as a function of the time $t$ (in s) is given by $i=0.10 \cos (120 \pi t+\pi / 6) .$ The voltage caused by the changing current is given by $V_{L}=L(d i / d t),$ where $L$ is the inductance (in $\mathrm{H}$ ). Find the expression for the voltage across a $2.0-\mathrm{mH}$ inductor in the circuit.

Carson Merrill · Accepted Answer

This problem 56. We see that the current is going to be given as a function of time. So we&#x27;ll have I equals zero 10 co sign of 1 20 pi T Plus. High over six. And we want to know um we want to find the expression for the voltage across 82 milla Henry in dr and we know that the voltage across the conductor is L. D. I. D. T. So in this case we take the derivative um we take the derivative across the induct. Er so that&#x27;s going to end up giving us if this was um alfa backs for example. And this was X. Then we know that if it&#x27;s lbgt we would take f prime of X. We take the derivative of the conductor but then we&#x27;re going to multiply that times two milla Henry, so 0.2 That would end up giving us our resulting expression for the voltage.

Sajin Shajee · Answer

determinative term in general five times Close a current weight easing simply using the differential equation five times coastline wire 20 which is which is represented as the as the voltage source, which is equal to five times I e plus your 0.5 partial I partial tea and I of zero. The current AT T equals zero is one. So by rearranging it, you have 100 ah, 100 games 100 times e to the 100 he co sign 120 t is equal to ah 100 i e of ah 100 gig plus e of wiring t part d of I key. So they play doing an integration on both sides to get partial intended he for I of t is equal for Barcelona. Powerful CI in terms of this 100 key here and then right Integrating on both sides you get you get I T V, which is equal to 120 sign 120 t plus 100 close sign 120 t ready by 234. Plus he turns eat a negative 100 I of zero is equal to 102 144 plus C, which is equal to one sees equal Don and 44 divide by 244. I have TV would then be able to through he find 61 signed up Iron Point T plus 25 divided by 61 curl sign 120 key plus 36 divided by six people I e of minus 100 thistles. Very part A and you use in calculate you lt which is equal to zero points here. Five partial I of tea, harsh ilk vigil. Then be equal. Teoh, which is equal to minus six. Sign 120 Cluster 79 to co sang our 20 G minus seven point Teoh heat of minus 100 e fired by two point or for

Ze-Han Lee · Answer

all right. Before this problem, we have Ah 21 8 Henry in doctor. And also it is, uh, connecting serious with 90 homes resistor in the 80 souls. So, uh, we already know Devoted your prostate doctor, is bl Here is the expression and we want to derive an expression for the body to be our across the resistance. Do that We need Thio. Firstly, look, look at the current in the circuit. So we four for Ah, a doctor. We know that Ah, the voltage leads the current least occurrence the voltage It is the current in that case. Ah yeah, we we confer yet we can firstly, the raft the amplitude of the current. Ah, By looking at this formula, we can see that angle for Quincy off the circuit is one Ah, it&#x27;s 14 80 rest for a second. So omega equal to one for zero reds per second and then we can derive the rack. Then something Doctor simply will be good times. L people thio to 66.4 homes What? And then ah, we can derive the current in the circuit so admitted with current amplitude equal thio Why not equal to them Picket of this 1 12 Hello, Derive. Divide. Ah, good bye. Bye. Oh, Miguel, which is to 66.4. So the answer is 0.0 45 half years. So this is the This is the amplitude And then we can be arrived The formula for the current in the circuit I equal to ay note times. Ah, yeah, because the curb, because the vaulting believes the current in the circuit And ah, specifically if we just look at the doctor Ah, the voltage will needs the current by pi over to phase. So in that case, we can ride the currents as, uh so this is negative. I not I&#x27;m Cy. One for you, One for a zero t minus. However, to Okay, so there&#x27;s this pie over to is the leading face from the from the from the from the difference of ah b and Ah, I so I I know he&#x27;s given here. It&#x27;s pointed 0 45 m peers and it was simplified. This the expression we find it April too. 0.5 course I 140 t Then we can utilize the arms law to find out the voltage across the resistance. So we are equal to ay times are Ari&#x27;s 90 olds. So result is 4.5 co sign 140 t. All right, if a party So I want to find out of e r and at this t equal to two minutes seconds. So we just need to pluck t equal to two times 10 to the negative three second into this expression and we can find out that we are at this time equal to negative 3.99. What&#x27;s okay?

Lucas Finney · Answer

So in this problem we have the voltage in a circuit with alternating current. It&#x27;s modeled by voltage of time. T is equal to 160 on E to the power of negative 20 t times coasts of 120. That&#x27;s not 120 to 120 times pi t where V is in volts and t greater than zeros in seconds. For part a want to answer what is the of zero? The initial voltage ovf zero going to equal 160 times e to the power of zero times coast of zero, which is just going to be 106 be. You don&#x27;t want to answer? What is the frequency? So we have frequency is equal to Pi nursery Omega over two pi Our omega is 120 pie. They have 120 pie divided by two pi. So we get 60. We have 60 hertz or 61 over seconds 60 oscillations per second, then lastly for part c Want to find V f T equals 100 graphically. So I&#x27;m gonna pop over to graphing calculator here writing out the equation. We have 160 times e The power of negative thio. Replacing or negative 20 rather negative 20 x where I&#x27;m replacing T with X times Coasts of coast of 120 pie x So we can see it&#x27;s oscillating very, very quickly there. But I&#x27;ll add on a horizontal line here and why equals 100 now I may need Thio adjust the appearance of the plot here because of how quickly varying this guy is. What? It&#x27;s not letting me let go. One moment here. Okay, so I&#x27;ll manually adjust this. Want to see from zero to about. It&#x27;s 105 so you can just see over where intercept. So it intercepts. AT T equals just about 0.228 So v f T equals 100. Pleasant T is equal to 0.228

Gideon Idumah · Answer

in this example we have on l c serious succulents with devoted source. You see records of 30 sign off 50 see votes we haven&#x27;t induct So l which is a ghosted suit number two Cherries. And then we have a capacity for C, which is a cost of 0.0 sufa rats. So we don&#x27;t have a resister because it&#x27;s just a out Elsie Serious succulents now want to find the currents in this securites? No, but we owe the fact that we know that you see the call to Q oversee. You have a ball He called all the eye that c so we don&#x27;t have a d o r no using catch us law. So using catch off slow the voltage law we have that&#x27;s all plus e c equality So hee So this implies that I have that our d I did see loss que overseeing it called Soon hee off. See now let&#x27;s plug in the volumes. This is my Alice tsu i d. I did see laws one over 0.2 cule you called 2 30 Sign off 15 c not recorded. I want to solve for eye, which is the Korans on. Do we have that? So recall That&#x27;s I called. So dick your ditzy. So what I do is I differentiate both sides of this questions. 11. Name this the question the question one cause I&#x27;m going toe combat seeds. So let&#x27;s different shit difference shits both sides off. One off a question one. Both sides both sides off one when in different ships Don&#x27;t. You&#x27;re gonna off soon. Discord. I did see squares loss one of ours. Oh, preserves. That&#x27;s 15 they have executed. See, which is I equals what differentiates e You have 1500 off course. Sign off 50. See Now I&#x27;ve used the fact that Dick you did see, of course toe are in the skin&#x27;s. So let&#x27;s more supply beside by Sue We have this squared I over did C squared loss. So I divide with that by destruction starts plus 25 I equality Several fut course signed off. See now the emergency question because we&#x27;ll solve this fourth of us off the Virginia spots The majestic question on as the auxiliary form on the auxiliary form off R squared was lost. This would be 25 r zero when solved these you&#x27;re gonna have. That&#x27;s this Implies that are oh, are squids? I&#x27;m is ours are squared equal to minus 25 are so that implies that are can be quote zero or are people too close of minors off five I now we don&#x27;t really need the results for our course is there because it&#x27;s not gonna lead us to anywhere. So we use this results. So that implies that I age off scene we called. So see one there because I don&#x27;t have a zero in classic on CDs. As Zero said, I would see one need to the zero sin, then co sign off five c lost. Sit to eat the zero c sign or five. T which I would rewrite us. I each of C I am a genius off people to see one call sign off five t plus so sign or five scene. Now, Next we use the method of on the timing coefficients is the method off undetermined coefficients. So find the particle a solution coefficient to find the particle of distribution, a participle, a solution. So that implies that we guess that I particle of c Let&#x27;s go about two things. Um because I have this 50 co sign of 50. See, so that my eye particle I will be off the form. It&#x27;s sun 52. Lost Be co Sign off 50 C Now I need to find what is the i p get see when it deflation issue off co sign off 50 C minus 50 bean or sign off. You did see it also needs disk. Would I pee off D C squared disappear. Also minus 2500. A sign off 50 minus 2500 being co sign off. See? No, I blood this log zoom because I&#x27;m looking for the particle institution. So plug into 11 in this equation. People shown soon. It&#x27;s so blood into soup. We&#x27;re gonna have duds. You&#x27;re gonna have just went out of my nose. 2500 a sign off. Usted si minus 2500 b. Who signed off 50. See? So this is this what I pleaded. See? Then loss. 25 more deployed by I. What&#x27;s my eye? Which is a sign off? Shifted scene lost be Kusenov shifted. See? There was said disability call to the right. Some sandwiches, several 50 off course. Sign off, Houston. See? Now, let&#x27;s go. Let&#x27;s like times together we go. I&#x27;m gonna collect it. Science to get out off minus 2500 loss than I have in 25 p. Oh, sign off. You could see on blows I have in mind. US 2500 lost. Identified. Off course. Side off. 50 C. Then this is all stiff records to several. 15 or sign off. 50 c. So what I do next is I quit my terms. I almost signed 50 see on the left inside. But I don&#x27;t have it on the rights inside, So that implies. That&#x27;s okay. These are boots, eh? So we add this through together, you&#x27;re gonna have that minus 2475 80 in court zero. So this implies that a record zero and that&#x27;s done now for B. When you add just it together, you&#x27;re gonna have minus two for 75 being now distribute the quarter 7 50 because they are both questions off Cassandra. 15. Seems so this across the seven. Sweetie, when cellphones these other B will be called to minor. Stand over 10 to 3. So this implies that&#x27;s my eye possible off. See, which is a gusto Es my zero plus be my bees Minus over. Budgetary on, then co sign off 50 c. All right, go. So the next thing to do is not to find. I&#x27;ll see. So that means I&#x27;ll see would be I am a genius of C plus I particular off scene. Now we add this to together. Go off. I&#x27;m a genetic dot that you see one who signed off five c plus. It&#x27;s to sign off five t that I particle. I was miners. Turn over. That three course signed off. You see now, Lemon named this question Question 30. Now we need to find what is C one on what to say to you. Now we&#x27;ve given that I 00 what? Zero. So that implies. That wasn&#x27;t I am zero bloody endurance of these. You have C one on, then this is zero on the minor. Stand over 33 and then this is 1/4 0 So that implies that my C one in court to 10 over 30. So we already got a bottle for C one. Well, now we need to get a value for six. Ooh, How do we get a value for seats? Room were also given that initial charge or zero. So we are also That&#x27;s cute. Off zero equals zero. No, we called us. Um um, you quote too. Oh, sorry. I didn&#x27;t call to do cute. Did you see? Now, let&#x27;s go back to one of the questions. We have the originally. So from equation one so that we&#x27;re gonna use a question one? No, from warm. We have that soon. Um, I primal scene laws 52. I often see equal to the O. C. Not receive. I wrote That&#x27;s rights. So after I&#x27;ve seen close, Yeah, one of those weapons who is 15 on then? This is I have seen because too. Um, you see, which is that&#x27;s his sign. 50 scene. Okay, so then just write this asked etc So this is 30. Sign off 15 c. So that implies that&#x27;s at sea, equal to zero. We have soup. I prime of zero. So this is one big question. One lost 50. I am zero equal to that sea sign. Zero. Now we are the IRS, a Boston zeros of these girls. So this Sunday And this is also zero. So this gold so that implies that I promote zero is also reporting zero. So this implies that I prime off zero, is also people to zero. Now let&#x27;s go back. That&#x27;s why. Limit those questions. So if you go back to question three so I need to just find different ships D&#x27;s actually equal to zero. It quits. It&#x27;s two equal to zero. So from Equus on three off that I prime off, see? Not as a call to minus five c wants signed. Five. Teen lost five seats. Who course sign of five t on. They lost 500 over that three sign off duty thing. No, we are I prime of zero quarter zero. So when I plug in zero, this is zero. This will be five See soon on then this will also be zero. So that implies that sea to import zero. Therefore, it&#x27;s implies that boxing push on three Which Israel I off is that I see it called So my c one is sent over 53 who signed off? I&#x27;ve seen my city zero and then I have minus turn over that theory course Sign off. 50 seen under communities in pairs

Christine Anacker · Answer

all right, We&#x27;re looking at a serious circuit now, if you don&#x27;t know what a serious sir, if it is, um, pretty much you got single pathway that carries a current where you&#x27;re ours. You&#x27;re resist. You&#x27;re Ellen. This case in the conductor, your beauty is variable, and your time here is measured in seconds. Now, we do have one equation that we&#x27;re using here. Does have to satisfy occlusion. Yeah, I already to you. Plus our over L uh huh. It&#x27;s people to one over l A times. So we are satisfying now for this case. They told us that our eye is zero. Our resistance is 100. Oh, are inducted ISS five memories on our variable voltage in constant fear at volts. And that&#x27;s me. So they want us to try to solve basically over new Israeli substitute in what we know. So we know that our 100 Oh, uh, one five times in cleaning that up that way. Divided by five one to you 12 So what we see now is we kind of have this occasion here. If I wanted to, I could actually change out this guy over on instead. You know what he does, I find. Because now it looks like our general inclusion. That was with your first order. So once we have that, we would know that are too. And find out our lower face, Any function, we would go in the power I want you, which happens to be you have power. Want teeth. Once we got that substituted into our equation the only difference here, why was I and that&#x27;s happens to be you? What&#x27;s up? You know, And with that exist, so end up with I go to the car one and we&#x27;re looking for the two going to a negative. You&#x27;re integral here and driven you still you. But that 20 would come down. We still needed to left over. We will divide that by two men that when the 20 comes down 12 divided by 10. Now we can go ahead and try to solve the equation. Or when it zero they have the power of negative. 20 times. Zero times you need a power 20 times row, Overton, plus our constant. So you have heard zero is one end up with one over one time lost my constant. And I need this guy to equal to Theo. It&#x27;s the only way for this equal to zero would be if 1/10 off something zero itself, Miss Hayes are see, value would have to be one giving us final equation. Even the power of you get 20 t and I worked. I don&#x27;t know if I wanted Thio 20 t over 10. We&#x27;re in this one time I could Oh, my brackets. And if I wanted to solve it in a way, or you might see it written a different way. So it could also see this written as one turns minus 1 to 10. 20 t over 10 and then from there. Or you might see it written as one Overton one minus you. The power of 20. Your choice. They all mean the same thing that would be solving that or those

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Solve the given problems. In testing a heat-seeki…

Problem 56 Easy Difficulty

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Allyn J. Washington, Richard S. EvansBasic Technical Mathematics with Calculus

Catherine R.

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Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus