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An RLC circuit is driven by an AC generator: The voltage of the generator is VRMs 96.8 V. The figure shows the RMS current through the circuit as function of the dr...

Question

An RLC circuit is driven by an AC generator: The voltage of the generator is VRMs 96.8 V. The figure shows the RMS current through the circuit as function of the drivina frequencv:900800600 100 200 300 400 600 dniving frequency (Hz)800What_is the_ohmic resistance of the RLC circuit? Please_ notice that the resonance curve passes through grid intersection pointSubmienswerTries 0/12If the capacitance of the capacitor is € = 409.0 nF; then what Is the inductance of the inductor?SubmienswecTries 0

An RLC circuit is driven by an AC generator: The voltage of the generator is VRMs 96.8 V. The figure shows the RMS current through the circuit as function of the drivina frequencv: 900 800 600 100 200 300 400 600 dniving frequency (Hz) 800 What_is the_ohmic resistance of the RLC circuit? Please_ notice that the resonance curve passes through grid intersection point Submienswer Tries 0/12 If the capacitance of the capacitor is € = 409.0 nF; then what Is the inductance of the inductor? Submienswec Tries 0/12 What is the power of the circuit when the circuit is at resonance? Submi Mswer Tries_OL1?



Answers

An RLC series circuit is driven by a sinusoidal emf at the circuit's resonant frequency. (a) What is the phase difference between the voltages across the capacitor and inductor? [Hint: since they are in series, the same current $i(t) \text { flows through them. }]$ (b) At resonance, the rms current in the circuit is $120 \mathrm{mA}$. The resistance in the circuit is $20 \Omega .$ What is the rms value of the applied emf? (c) If the frequency of the emf is changed without changing its rms value, what happens to the rms current? (W) tutorial: resonance)

First of umbilical Cleared angler is an inter frequency off RLC series circuit. By using the relation angler present and frequency equal toe. So get a load off one divided by induct ins Times get the stones putting different values here one divided by here Independence of the cities zero point 300 Henry and keep distances 16 My girlfriend it 36 times 10 to the power minus six Fettered this use US angler Resonant frequency equal dough 700 45 Radian Worse again In the next part we want to calculate resistance it residence imprudence off our city circuit is equal dough resistance so we can write recent sequel Toe Imprudence s impotence is a ratio between spiegel days applied source Do you add it by speaker here people Dish of the sources 400 40 world divided by speaker in the circuit is zero point 56 in peer This gives us ready since equals toe 700 and a six home living The last abad of this problem We want to call cleared equal days across register in Dr on the campus ter big wattage across register physical do speak Earn times registers here be current is zero point 5 60 ampere and reticence is 700 and the six home This gives us big, old it across resistor equal toe 400 40 world big old age A grass in doctor is he could do speaker times The intense off in Dr That is it will do. I times the Agence off in Dr Ed ordinances equal toe angler resonant frequency times indoctrinates the physical toe I in tow. Resonant difficulty off RLC series circuit is so good old off One divided by Ellen Do see Excuse us I in tow. So get a load off El Suker divided by L C as we can, right? L equals toe. Secure it off, So get off l So this gives us big will teach across in doctor Equal Toe I into so get it off. L divided by, See? Nope. Electing different values here We currently is zero point 56 and Pierre into secure it off. Ellie. Worried by sea here in doctrine C 0.3 Henry, divide by get distances. Six microfiber date is six times 10 to the power minus six. Fettered. This gives us big voltage across in Doctor equals toe 125. Well, IHS, add resonance but he attends up in Dr Is You could do react prince off Cape Mr So therefore well dangerous in Dr is us ical toe were detected us get Mr So we'll take a grass That is big voltage across Get Mr is the US equal toe 100 25 world

High in the given problem here. This is a series R. L. C. Circuit. First of all there is a resistance then there is an in doctor called and then at last there is a capacitor all joined in serious combination in the circuit and then there this is the source of alternating will teach like to eat the terminals martin as a and be and see and be here. The value of arms potential applied is 414 fold. The value of resistance is 250. Or Self independence is 0.00 Henry and capacitance is 2.2 Micro. The addict. Now in the first part of the problem we have to find resonating angular frequency which is given by the expression. Only the note is equal to one by and the root L into C. So plugging in holland values here. This for me or not will be given by One divided by the square root of self independence which is zero wind 800 Multiplied by capacities which is 2.2 into 10 for -6 which comes out to be one by 1.33 Into 10 dish part -3 Radiant per second. And finally answer for the first part of the problem is approximately 750 radiant for a second. Which is the answer for the first part of the problem. No. In the second part of the problem we have to draw a phaser diagram for the situation. So to draw the fees er diagram, we showed the army's potential top taking place across resistor long X axis and that a gross in doctor he's shown a long positive Y axis and that across capacity is shown along negative Y axis. So here this is we are, this is the L and this is we see no first of all we find no up to you reactant which may be equal to capacity reluctance also. And that will be given by the expression for Megan would help for the inductive RIA tense. This expression will be but actually it will be valid for ecstasy also because there is resonance in the circuit. So when we put the values for omega not this is 750 radiant, But second multiplied by 0.800 Henry. So This value comes out to be approximately 600 home. So both of these reactions is are having the same value and the impedance of the circuit will be simply equal to resistance only because Excel physical to ecstasy and that is given by eggs l minus ecstasy to the whole square class R. Squared. So as Excel cancel out ecstasy. So the remaining ingredients will be equal to resistance only. No. In the 3rd part of the problem we have to find the potential drops across various dominance given. So first of all we have to find B. B. And here. If you look into the circuit, we may be means they have to find potential drop taking place across injector. The means we take that will be given by. I'll be into Exactly for I. D. It will be equal to the armies divided by net resistance, which is equal to our own me into exile. So for Vietnamese, this is 440 world for artists is 254 multiplied by exile Which is 600 so this we a B comes out to be Approximately 1.1 kilo volt one sir. First answer for the third part of the problem and the same third part of the problem we have to find we Bc also and that BBC is actually equal to be Yeah, this V A. B is equal to we are as this is the resistance and this is the conductance practices the capacity. So for a disease. Not really. This is we are. So this is ivy into well means this is 440 into 2 40. Multiplied by, divided by 2 50 multiplied by again to 50. So finally, actually this really is equal to the total potential applied because all the potential applied is is dropped across the resistance. Only more work here. We also we will have to change that is our again saying this. So this is equal to be A. D. Equal to 444 to only now for BBC this is equal to be means I. D. Into Exactly for I. B. Again, this is 440. Divided by 2 15, multiplied vibe. It's a. Which is 600. And this time it will come out to be Equal to 1.1 kg vote. Second answer for the third part of the problem. Then in the same third part of the problem, we have to find V. C. D. Also which is nothing but equal too busy. And that will be equal to as it is equal to I've been to as a ecstasy and X equals to each other. So this we C. T. Will also be equal to 1.1 global. The turn answer For the 3rd part of this problem. And now we have to find we A. We have to find BBg. And if you look at the sweet VD from here to here, this will be the L. E minus species. And as both of them are equal. So yes, we Bdb equal to be a minus B. C. Means this is zero, Which is the answer. 4th answer for the third part of this problem? No. In the 5th part of the problem, in the 4th part of the problem, if you are is replaced by under the resistance those values 125 homes, they have to find a change taking place In the resonating frequency. But as this f not is given by one x 2 by in Dental C. There is no role of resistance in the circuit hands. This frequency will be insane. As 750 radiant percent and angular frequency. North to frequency. Thank you know, frequency. Well, we've been seeing no in this case. In the last part will provide the current army's current passing through the circuit. So that will be given by the army's divided by art. The army is 440 World Pakistan. The current is 125 so I RMS now comes out to be 3.5 to m. B. A, Which is the answer for the third, which is the 5th and the last part of this problem. Thank you.

To complete the reactors. We only have to remember that I are. A mass is equal to one over the reactor's times V are a mess. Then so be for the reactor's Get that the reactor's Izzy close to V ROMs divided by I a mess. Then, using the data that was given by the problem, we get that the reactors is opposed to 0.8, divided by 0.515 mealy and piers, Um thes is approximately 155 treat homes, and we can write it as being approximately equals to 1.6 kilo Holmes. To copulate the capacitance, we have to remember that the reactant is given by one divided by two pi times the frequency times the capacitance. Then the capacitance is given by to pipe times. He frequents times the reactors. No using our intermediary result for the reactor's on DDE. The initial data given by the problem we have a capacitance that he's given by one divided by to pie times the frequency where is too kilo hurt times the capacity of the reactors, which is 0.8 divided by 0.515 I'm Stan put in my industry at the Z Z equals true um, zero 0.515 time stand to the minus tree divided by two pi times two times stand to the third times 0.8 and this is approximately 5.1 times 10 to the minus eight for its and it can be reading us 51. No, no for its Finally, for the last item, we just have to remember that there are a mess. Current is proportional to the frequency of the sewers. So in the first case there frequents off the source is more to play it by a factor of two. Then the R. M s current in this case will be the R. M s current in the previous case to play it by two. So the R. M s current here is two times 0.515 which is equals true. One point. This is the road tree, really m peers. And finally, in the last case, we have a frequency that is 10 times bigger. Then they need show frequency. So the r m s current here, we'll be equals to 10 times. They need show every mess current and these easy goes to 5.15 million amperes

Resonant frequency. F not equals Omega not over to buy. It was one of our toe by times one over squared off l c. So now putting the values in. We have God to buy squared off as it was 40 million Henry and Kappas Disease 0.5 Fat odd in verse off that So gas, including this comes out to be 3.56 hearts.


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