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A1) A coil of resistance 52 and inductance 120 mH in series with a 100 UF capacitor is connected to a 300 V, 50 Hz supply: Calculate a) the circuit impedance; b) th...

Question

A1) A coil of resistance 52 and inductance 120 mH in series with a 100 UF capacitor is connected to a 300 V, 50 Hz supply: Calculate a) the circuit impedance; b) the current flowing; c) the phase difference between the voltage and current; and d) the voltage across the capacitor; (5 Marks)

A1) A coil of resistance 52 and inductance 120 mH in series with a 100 UF capacitor is connected to a 300 V, 50 Hz supply: Calculate a) the circuit impedance; b) the current flowing; c) the phase difference between the voltage and current; and d) the voltage across the capacitor; (5 Marks)



Answers

An RLC series circuit consists of a $50-\Omega$ resistor, a $200-\mu \mathrm{F}$ capacitor, and a $120-\mathrm{mH}$ inductor whose coil has a resistance of $20 \Omega$. The source for the circuit has an ms emf of $240 \mathrm{V}$ at a frequency of $60 \mathrm{Hz}$. Calculate the ms voltages across the (a) resistor, (b) capacitor, and (c) inductor.

Will induct INS L is equal to 150 million Henry. 150 million Henry and then ca best ins see welcome bastions equals five micro fear. Odd, right and frequency after is equal to 50 hearts and maximum will teach. Maximum voltage is equal to 200 um 40 Walt and maximum current is equal to 100 milli ampere, right? So let's to marquis. Well, conductive reactions is Dubai f times l. And by substituting values, we have 100 pie multiply by 150 multiply by 10 to the dollar minus three. And then I use this 47.12 arm 47.12 arm that the inductive reactions now in part B. We'll find out the capacity of reactions incapacity. Pre actives is one divided by 25 times the bastions and by substituting values. Now 10 to the power six comes in the numerator and then one member pi multiplied by five. Therefore, capacitive reactors is 636 point six to home and no parsi. Well, impotence that equals maximum will teach, divided by the maximum current and maximum will teach 240 uh, divided by our maximum current is 100 million peers. So the Milly factor comes in the numerator tend to the fallen tree and therefore the impotence is two point for kilo. Oh, right, and no, let's to part D now we do party here, So these are d well, impotence that is equal to square root wolf our square less x l minus xy whole square. And by substituting values well, that impotence sees 24. I'm great right square, and I am taking squid on both sides as well. Then are square less XL minus accidents of 47 0.1 to minus 636.62 old square. And from here, resistance R is equal to 2.3 three kilo. Oh, him right. And finally we find out, um, defy. Right, So this part E now this one is body right now why is equal to buying is equal to game in worse now off x l minus x c divided by r and therefore by substituting values fine comes out to be 14.22 depres

You bought area Ross Tickle play, too. They induct you in Dr Reactions Reactions X l, which is equal to two pi f l so two times 3.14 times the frequency or 50 hearse times inductions off 0.150 Henry. This gives us the inductive. Keep Americans off 47.1 arms I want to be Our capacity reckons Exceeds, given by one over to buy guns frequency times capacitance Some student values. Two times 3.14 times fifties frequency times five times 10 to power minus six is the capacitance. This gives us 637 forms. What? See the impotence off a circuit is Z is equal to re Max, derided by I'm Ex Walters maximum divided by current maximum Walter tracks where we have is 4 to 40. Divide by 0.100 This gives us 2 40 0 Holmes is our impudence, but D weekend ah find the total impotence for circuit That is easy. Cool, too. Our square plus excel minus Pepsi's where substituting your values study nor the impudence will find resistance. Rather, we only found the impudence here, so simply find this expression for resistance. Resistance we get here is ah z square minus excel minus X C square. So substituting a values Zeevi found easier to 400 square minus Excel is 47.1 minus sees 3 67 square. This gives us the resistance off 2330 owns but e the fans angle is given by that, uh, thing in Warsaw for X l minus. Exceed divided by our distance since obstructing your values. Taking in wars Here 47.1 minus threes through your 6 37 divided by 2 33 2 33 Ah, this gives us an angle off Fez Ingle, off minus 14.2 degrees.

Belongs to the alternating current chapter in which we have V. RMS equals to 1 20 world. And frequency F equals to 60 hertz of an Rlc series circuit. Having resistance R equals to 1 50. Home inductions. L equals to 1.20 million Henry. And capacitance equals to 33.5 micro ferret. Okay so for the part of the question we have to calculate the reluctance of the capacitor XC and for the conductor L. X. L. Okay so The X. C. It will be equal to one x 2 by F. See so substituting values so we get one by two pi multiplied by frequency 60 hertz and capacitance is 33.5 micro forever. That is 10 to the power minus 6 30. So from here we get exceed that is equal to 79 point double two home. And similarly excel. That is equal to two pi F. L. So two multiplied by frequency is 60 Hz. And in defense L is 1.20 into 10. To the power minus three Henry. So from here we get X. L equals two. G 0.45 double two home. Okay so this becomes the answer for the part that is capacitive leah tense and that is inductive resistance. Okay now moving to the part B in which we have to calculate the impedance Jed and which will be equals two. R squared plus X. L minus X C. Holy square. And this under oath. So substituting values so we get Jerry equals two our which is 1 50 home. So Holy Square plus XL which is 79 point double two minus X. C. Which is 0.45 double two. And this holy square and this understood. So from here after solving impedance jed this will be equal to 1 69.4 home. So this becomes the answer for the part B. Now for the party we have to calculate the peak current so it will be equals two. We not by jail. And we know it can be written as under two times of the RMS divided by gender, so substituting values. So under the tumor we note which is equal to 1 20 Volt. They were major, which is 169.4 home. So from here we get peak current. I not equals to nearly one point double zero mps. So this becomes the answer for the part C.

All right, We're given some information here. We have a resistance of 150 Holmes, we have an inductive since of 250 million. Henry, we have a capacitance of to times 10 to the negative Sixth power Farid dealt of the max. His 210 volts frequency is 50 hurts. So what is the inductive react? It's well, inductive reacts. The reductive inductive. Reactant is omega L, which would be two pi f l. So putting that into a calculator to hi 50 kinds 0.25 is l 78.5 O's b is asking us for the capacitive react. It's one over Omega Psi, 1/2 pi FC. So putting that in a calculator one over who does probably has 50 kind of the capacitance, which is two times 10 to the negative. Sixth power 1590. Oh, what is the impedance? This should be a see down here. Pretty sure I tried to write it as a C uh, that's going to be the square root of our squared plus x l minus. XY squared a little bit surprised that X C is so much larger than X L but let me just double check my calculations. 50 hertz tube times 50 times. L uh huh. One over to pay off. I'm see which is two times 10 to the negative sixth. Okay, I'm gonna put that into the calculator. Square root of R squared. Which 150 squared? Um, X l, which is 78.5 minus 1590. Squared, 1520. All right, now we need the maximum current. Um, current max is Delta V Max over Z. So putting in Delta V. Max, uh, 210 who can over Z 0.132 amps. 132 millions. The phase angle, the phase angle is the inverse tangent, X l minus X c over our. So putting that into a calculator XL minus X C over 100 50. Negative. 1.47 Okay, that's in radiance. They're showing an answer and degrees, which is not gonna be the same. Is that so? We just change it to degrees. Oh, yes. It ISS 84 0.3 degrees Negative. 84.3 degrees


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