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When 2.5 micro-F capacitor (s connected to a generator whose rms output Is 120 V, the current in the circuit is observed t0 be 1.2 A The capucitive reactance...

Question

When 2.5 micro-F capacitor (s connected to a generator whose rms output Is 120 V, the current in the circuit is observed t0 be 1.2 A The capucitive reactance

When 2.5 micro-F capacitor (s connected to a generator whose rms output Is 120 V, the current in the circuit is observed t0 be 1.2 A The capucitive reactance



Answers

A capacitor is connected across the terminals of a 115 $\mathrm{V}$ rms, $60.0-\mathrm{Hz}$ generator. For what capacitance is the rms current $2.3 \mathrm{mA} ?$

I wrote down the information that is given, and the first thing we have to do is figure out the react. It's the reactant since is one over Omega Psi. I underlined omega in green and C is the 25 times 10 to the negative six power parrots Putting that in a calculator. I get 10.6, which I'm going around to 11. So part B. Ah, an expression for the current. Okay, the current as a function of time, we could differentiate the charge with respect to time, but we're going to get Omega Psi V subzero sign of Omega T plus pi over two. That gives us omega is 120. Pie see is 25 times 10 to the negative. Six. Power parrots. Um V zero is 100 60 volts. Sign of 120. Hi. To plus pi over two pi over two comes from whom we take the derivative fruit of Of the sign is the coast. So, um, putting some of this into the calculator 120 pi times 25 times 10 to the negative says six power. Yeah, that would be six power. Yeah, 25 times 10 to the negative six. Makes me wonder if I made a mistake in the previous in part a gonna do that again later. 120 volts. You're 60 volts in this. Putting these three together gives me 1.5. Uh, sign 120 pie T plus Hi. Over to, And that's going to be in amps. All right, so now I need to go back to part A Because I think I made a mistake taping this in one over 120 pie. 25 times. 10 to the negative sixth. So let's try this again. That should actually be 100 10. Okay, that's it. So thank you for bearing with me.

For the human problem in order to find a frequency. Well, first, find the V max maximum voltage. And from there we'll find the reactions. And then ah, Saul, for musical to one or two by ex, huh? React inst times capacitance where capacitance is given. So we max is equal to square root off two times. We are a mess. Our message even we have is a 30. So two times already two times world off. Two times in 30. This gives us 42.43 watts. Or from here we can find the easily wrapped in Seoul Reacted to the ReMax divided by I Max I'm x is given. So we matches for 2.43 divided by I'm X. Is there a 0.30? And peers? This gives us ah reactions off 1 41.4 homes. Well, substitute this value here and substitute the value for capacitance. So let's do that, eh? Physical to one. Over to the 3.14 times. One for one point. Four times of Sebastian's. Even we have easy for micro Karadzic minus six. This gives us frequency off 28 2 280 Hurts

Hi. In the given problem, then a d C. Direct current passes through on in Doctor Call, having a value off 2.5 ampere after applying a battery which supplies of old age or 36 water grows it. The resistance offered by the wire used to make this industry coy maybe even by own slow as we by I r equals three by I. So this is 36 by to fight, which consult will be 14.4 home. So this is the answer for the resistance off the in Dr COIT? No. Then and a sea world age is applied across the coil We a Jew me Toby RMS value which is given to us and that is 1 24 Then Artemus Gordon passes through the score having a value off 3.8. And here applying again, the arm slow at crows. This coy, we get the value off net impedance offered by the score. So it comes out to be the ratio off the RMS by I Arness, which comes out to be 1 20 by 3.8 and it becomes 31.6. Oh, this is a value off the impedance. No, we know the relation for this impotence in terms off reactant offered by the oil and resistance off the circuit artist way. So using this, we find an expression for the in depends for the reactant offered by the boy which is square Trudeau. Very square minus already square. So you can say this is to buy F L, which becomes 30 square means 31.62 The whole square minus are square means this is 14.4. So the whole square and it comes out to be This is 998 0.56 minus 207.36 and this difference comes out to be 791.2. So finally, this self independence, the expression for self independence comes out to be the square root off 791.2, divided by two by f f is the frequency which is given as 60 hertz. The square root of this 7 91.2 comes out to be 28.13 and this is the writer by two into 3.14 into frequency, which was 60. So this value off. Self Independence comes out to be 0.746 500. All we can see Toby seven 0.5 in tow. 10 dish with the power minus two. Henry, this is the value off the self in the tense off the oil. And that was the resistance off the oil r equals to 14.4 room. So these are the two required answers off the given problem. Thank you.

So in this problem, working Serena's circuit and sees offers his store on any doctor getting Siri's with R A C generator so called volume inducting its European security to Henry's. The generator has everyone's of 100 to be hurts on a voltage of pink polls. Andi was given to voltage across the doctor. He stood by six votes and we want to find the value of the resistance. So pretty minuto crying. Okay, Since it turns out it isn't serious, it is Sankaran forever for every element. So the car into circular please have the, uh, old is helping Dr Divided by the inductive reactions on we tried. Probably expression for the top reacting this we have this way. No, the Wallabies. Well, that's 2.6 No f hell. So I just get so current of syrup on what appears flowing through the whole city. Now we're gonna find a voltage across her sister by using just following relation issues, particularly the orienteering on double just for her sister's piece square root off the voltage of the generator. Zero squared minus the voltage across. The doctor squared the square with that That gives us a voltage of seven points exposed on across the resistor, a dead resistance accused ratio off the cultish undercurrent, and it feels about for subsistence off $76.


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