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Question 32 pts8 sin(ot)circuit is constructed with an AC generator; (eslstor, capacitor and inductor as shown. The generator voltage varies in time as € Ensi...

Question

Question 32 pts8 sin(ot)circuit is constructed with an AC generator; (eslstor, capacitor and inductor as shown. The generator voltage varies in time as € Ensinut; whcre En 120 Vand 695 radians/second: The values for the reraining circuit components are: R = 600,L 121, mH, and € 13uF, Find the maximum voltage across the capacitor; Give your answer t0 3 significant figures; in volts:

Question 3 2 pts 8 sin(ot) circuit is constructed with an AC generator; (eslstor, capacitor and inductor as shown. The generator voltage varies in time as € Ensinut; whcre En 120 Vand 695 radians/second: The values for the reraining circuit components are: R = 600,L 121, mH, and € 13uF, Find the maximum voltage across the capacitor; Give your answer t0 3 significant figures; in volts:



Answers

An inductor $(L=400 \mathrm{mH})$, a capacitor $(C=4.43 \mu \mathrm{F})$, and a resistor $(R=500 \Omega)$ are connected in series. $\underline{A}$ $50.0-\mathrm{Hz}$ AC generator connected in series to these elements produces a maximum current of $250 \mathrm{~mA}$ in the circuit. (a) Calculate the required maximum voltage $\Delta V_{\max }$ (b) Determine the phase angle by which the current leads or lags the applied voltage.

In this problem on the topic of inducted its we're told that a capacity that is charged and has a rating of 590 micro Farage's is connected to an in doctor in series and then doctor has a conductance of 0.33 Henry's. We want to know what the maximum voltage across the capacity use if we know that at an instant when the current is one is 2.5 mps. It is increasing at a rate of 73 mps per second. Now the total energy shared between the induct er and capacitor and the potential across the capacitor inducted as always. He's always the same which means that Q oversee is equal to all times the absolute value of the eye. T. T. The capacitor energy is huge squared over to see the conductor energy is a half ally squared. So the total energy E. Is equal to Q squared over to see plus a half hour I squared. And this is the maximum energy stored in the capacitor which is Q max squared over to see which we can write as a half. See V max squared. Now the charge Q. Is equal to how M. C times the I. D. T. And so this is the inductions. Zero point 33 Henry's times the capacitance, 5.9 times 10 to the minus four. Farage's times the rate at which the current is changing the I. D. T. Which is given as 73 amperes per second. This gives us the current Q to be one 0.4 to one times 10 to the minus two columns. Now that we have the charge, we can find the maximum energy which is a half. See V max squared which is key squared over to see plus a half hour I squared. And this is one point 4 to 1 times 10 to the minus two columns squared, divided by two times the capacitance, which is 5.9 times 10 to the minus four, Fareed's lesser half into the induct inst zero point 33 Henry's times the current 2.5 mps squared. This gives us the maximum energy to be 1.202 jules. And using the maximum energy we can find the maximum voltage across the capacitor. V max is equal to the square root of two times this maximum energy 1.202 divided by the capacitance C, which is five 0.9 times 10 to the minus four ferrets. This is 1.202 jewels. And so if we calculate this, we get the maximum voltage across the capacitor to be 63 0.8 volts.

Per day. We know that the inductive reactors is gonna be equaling two pi times the frequency times the inducted. This would be equaling two pi times 50.0 hurts multiplied by 400 times 10 to the negative third Henry's. So this would be equaling 126 times the inductive, the capacitive reactor it's rather would be equaling one over to pi times the frequency times the capacitance. This would be equaling one over to pie multiplied by 50.0 hurts multiplied by 4.43 times 10 to the negative sixth Farage's and this is equaling 719 homes. And so the impotence Z would be equal in the square root of R squared, plus the inductive react. It's minus the capacitive reactor is quantity squared and this is equaling square root. Ah, 500 homes, quantity squared plus 126 minus 719 quantity squared and then comes squared. And so this is equaling 776 rooms, so that would be the impotence. And then to find the maximum voltage, this would be equaling the maximum current multiplied by the impotence Z. So this is the equaling 0.250 amps multiplied by 776 rooms. And this is giving us 194 volts for the maximum voltage four part B. Then we can say that five's gonna be equaling arc. 10 of the inductive reactivates minus the capacitive reactant CE divided by our and the same equaling are 10 of 126 thumbs minus 719 comes find it by 500 homes and we find that fives equaling negative 49.9 degrees. So this means that the current leads the voltage by 49.9 degrees. This would be our final answer for part B. That is the end of the solution. Thank you for watching.

The total energy issue between the doctor and the capacitor. The potential across the investor and in doctor is always the same. And qc que overseas ableto l d I The domestic energy excuse Great over to see And they knocked energy the half l I square. So the total energy is given by the for expression. So Q squared over to see best 1/2 Oh, I swear is equal to the maximum charge How dmca Bester squared your next grid over two times its capacity to see this is equivalent to a heart that would be next. Square the maximum voltage across the best way to reach the soulful so fussy before we solve this equation When you distort que from the initial equation. Q. Is how time see, and the I you cheap and these values all known. So that's inductions off zero point 33 Henry, So it's oppressed the units here. The best chance is given as 5.9 tends to into the minus four. So that's the current is changing at a rate off 89. NPR's for second, and so we get the challenge, que to be one 0.73 I'm Stan to the minus two. Cool owes what? Now that we have the charge, we can go back to our equation. So we get that Ah ha. See, V squared is equal to que which we calculated to be one 173 times 10 to the minus two. Goodbye, Goodbye from time to questions just to into five, 49 times 10 to the minus full for its Actually this is your script and then the other time is a hot and induct int l, which is zero point the three Henry's. I want you glide by the current off 2.5 and piers squared. And so how I see the squid Max actually is equal to one want to a six Jules and therefore this makes it easier to find or value for the Mets. So the Mets is simply this. We're route to times. This value 1.2 86 tools divided by the best in C 5.9 pence, 10 to the minus full parents and begin the maximum potential the next voltage across the Avesta 66 and by energy conservation, the maximum potential across the in dr will also be 66 falls. But you could, at the instance when the capacitor is charged

In this question, we have this um are sees the kids. We need to find the impudence of the circuit, maximum current and the phase angle between the current and voltage and then determine whether the current uh leads or lack the footage. All right. So to do this question for part A to find the impedance, he will be using Z is equal to our square plus X l minus X C. Square and square roots. So uh and Excel is equal to omega L. Which is two pi F M L. So we can compare this 1 1st Two Pi Times 240 times 2.5. And value is yeah 3770 homes. And then the X. C. Is equal to one of omega psi, which is 1/2 pi F C. To substitute the numbers two pi times 2040 0.25 times 10 to the Power -6. And the capacity reactant is 2650 Holmes. So to complete the impedance, Z is equal to 900 square plus 3770 -2650 sq in spirits. Okay. And the answer is 1.43 kg owns. Mhm. Next in part B. We want to find out maximum current. So I. M. X. Is equal to remax. Uh The Rabbi Z. And this question, the B Max is 140 and then divide by 1.43. Uh thanks 10 to the power tree. And the answer is 0.0979. and pills in policy we want to find a face anger. Can you be using hi equals to our attention. X l minus X E. R. So just substitute values. I remember 3770 minus 2650 Dubai by 900. Okay. The answer is 51.1° and then in paddy sci fi is positive. Mm. Okay, voltage. Yeah, Late current. Mhm. All right. So that's how we solve this question and that's all


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