an-r-c-circuit-consists-of-a-resistor-r32-omega-a-capacitor-c25-mu-mathrmf-and-an-ac-generator-with-

Question

An $R C$ circuit consists of a resistor $R=32 \Omega,$ a capacitor $C=25 \mu \mathrm{F},$ and an ac generator with an rms voltage of 120 $\mathrm{V}$ .
(a) At what frequency will the rms current in this circuit be 2.9 $\mathrm{A}$ ?
For this frequency, what are (b) the rms voltage across the resistor, $V_{\mathrm{rms}, R},$ and $(\mathrm{c})$ the rms voltage across the capacitor, $V_{\mathrm{mss}} c^{2}(\mathrm{d})$ Show that $V_{\operatorname{mss}, R}+V_{	ext { rms }, C}>120 \mathrm{V}$ but that $\sqrt{V_{\mathrm{rms}, R}^{2}+V_{\mathrm{rms}, c}^{2}}=120 \mathrm{V}$

João Gabriel Alencar Caribé · Accepted Answer

the first tight and we can use all those law to relate the voltage with the current as follows. The re mass is a coastal y You&#x27;re a mess times impedance then they are in mass current. Is it close to the ari mass politics divided by the impudence? We want the currents to be cost 2.9 amperes. So 2.9, we will be close to 120 divided by the impedance. Therefore impedance is there any cost to 120 divided by 2.9, But they beat us in. The situation is equal to the square root off R squared, plus the capacity of reactors squared from these easy close to 120 divided by 2.9. We also know what is their value off the resistance. So we can blogging in this equation to get square root off. 32 squared plus XY squared square root is it close to 120 divided by 2.9 square in both sides and sending the storm to the other side. We get XY squared, he&#x27;s equals to 120 invited by 2.9 square miners, 32 squared and finally we get that XY is equals. True, the square root off 120 divided by 2.9 squared, minus 32 squared. Not that we&#x27;re not considering their negative square root because there are no negative react. Ince&#x27;s now remember that the capacity reactors isn&#x27;t close to one divided by two pi times the frequency times the capacitance. We want to know what is the value off the frequency then we saw for the frequency needs equals to 120 divided by 2.9 squared minus 32 squared Solving for the frequency as easy as sending this with the other side and leads to decide So we got frequency is equals two to pie times the capacitance Times Square Eat off 120 divided by 2.9 squared, minus 32 square under one. Finally, we can plug in their value off the capacitance to get their value for the frequency. What the frequencies in close to two pi times the capacitance, which is 25 times 10 to the minus six because it&#x27;s, um, Negro for it. Times the square root off 120 divided by 2.9 squared, minus 32 squared. And these is approximately zero point 24 kilo hertz. For the next item, we have to complicate what is There are immense voltage across the resistor governments voltage across the resistor is he calls too. The r E m s current kinds. The resistance of the resistor, which is equals two 2.9 times started to which gives us a narrow master politician off 92 0.8 votes, which can be approximately 2 93 worlds on the next time. Then we have to complete what is the R. M s voltage across the capacitor and these is equals to the R. M s current times the capacity reactors, because he goes to 2.9 times one divided by two pi times 0.24 times 10 to the third time&#x27;s. The capacitance witches equals to 25 times 10 to the minus six. And this is approximately 76 votes. No, on the last item. It&#x27;s very easy to see that V. R. M s across your resistance plus Vieira mass, of course, like a pass it or is it close to 93 plus 76 which is it goes to 100 and 69 votes, which is bigger than 120 votes. But on the other hand, a square root off via a mass squared across the resistance plans Vieira Mass. Of course, they could pass it towards Queer is equal to the square root off 93 Squared plus 76 squared, which is approximately 120 votes.

João Gabriel Alencar Caribé · Answer

we begin this question by remembering the relation between the aromas voltage on the R. M s current. So the remans voltage is equals to the art room. Ask current multiply abiding Penis of the circuit. Them they be That&#x27;s that&#x27;s very good is it goes to the arguments voltage divided by the r. M s current. And now we remember that the impedance off the circuit is equal to the square it off. The resistance is cleared plus the inductive reactors squared and they took The reactant is equals two to pi times the frequents times named look tense squared Then we can solve for the resistance to get that their existence is in question. They feed them too. Square miners to five f l squared under a square root No, we can use our previews result to get that the resistance is it cost to the square root off the ari mass divided my eye ROMs squared minus two pi times the frequency times they looked at us squared, then plugging the values, giving any problem we get that the resistance is close to the square it off 25 divided by 0.26 squared minus too high time. 16 times. 145. Really, Harry. So come to the ministry here, square it. And finally, the resistance is approximately 79 hoes. In the second item, the voltage across the resistor is given by V. Hiram s across the resistor. Is he? Of course, too? The current that flows through the residue store times their insistence off that resistor Then the voltage across the resistor is given by, uh, zero 0.2600 years times 79 homes. And this is you close to 20 point 54 votes. The IRA mess Voltage. A crossing doctor is given by the R. M s across the doctor is he goes to the current that flows fruit in Dr Times, the reactive in doctors and this is their clothes too. Zero points 26 times to pipe times the pregnancy, which is 60 hordes times l conductors, which is 100 45 times 10 to the minus street because there is immediately prefix there. And all of this is approximately 14 point or anyone votes? No, we should evaluate the following quantity. The Squires off the are a mass from the resist or squared. Plus there I remember from the doctor squared, these is equal to the square root off 20.54 squared plus 14 points, 21 squared. And this is approximately 24 point 97 which weaken further. Approximate to 25 votes, then square root off V. Hurry mass. Through the reason Stan squared plus the remans voltage for the Doctor Square. Is he close to the remans? Voltage off the source.

João Gabriel Alencar Caribé · Answer

to solve this question. We begin by using the following equation V. Our romance is he goes through i every mass times z where the is the evidence off the circuit. This is a version off homes role that is valued for arson circuits and engaged have forgot impedance off the circuit is given by the square root off R squared plus exceeds squared. These is the resistance on disease. The reactors the reactor&#x27;s is given by one divided by true pi times the frequency times the capacitance. So putting it all together and solving for the current we get I Every mass is. He calls, too. Our romance divided by the square root off R squared plus to pie see under one squared, no plugging their values given by the problem. We got square root off 10 times. Stand to the third because there is a kilo of warm there and I&#x27;ll do the squared plus to pie piously frequency 125. Hundreds times the capacitance 0.25 me crow fired soldiers attending the minor six. Here we didn&#x27;t have one. I already squared is all under the voltage, which is 42.5. No solving that calculation. We got zero point 00 30 seven nine approximately, and we can write it as tree 0.79 Really, m peers.

João Gabriel Alencar Caribé · Answer

to complete the resistance in the circuit. We begin by calculating the impedance off the circuit so we can complete the impudence by using the adopted version off as well. So v are a mess. He&#x27;s equals two. Why are a mass times the impudence? So thank you. This is equals two V. All right. Mass divided by right. I remember plugging the value is given by their problem, these one in these one we got 95 divided by 0.722 And now we remember that impedance is given by the square root off the resistance squared plus the reactant squared. The reactant is one divided by two pi times the frequency times they could pass down squared. Then from these equation we get, that is this word is equals two R squared plus to buy See under one squared. Now we can solve for the resistance to get our is equal to the square. Root off these weird minus to buy F C under one squared, then plugging the value we have calculated for the peters and the order values given by the problem, we get that the resistance is equals to the square root off 95 divided by 0.72 squared miners to PI times 150 times 13 meat group. All right, and this is all under one and squared. Finally, By solving the equation, we&#x27;ll get that the resistance is approximately 103.6 to serve them homes.

João Gabriel Alencar Caribé · Answer

to solve this question, we have to complete what is the current that flows for the circuit. And to complete the current, we have to complete the impedance and to Copley impudence. We have to complete the react tenses. So we beginning by calculating the capacity of reactors, which is given by one divided by two pi times the frequency times they capacitance and these easy close to one divided by two pi times 60 times 0.12 time Stand to the minor. Six Because there is a micro there, and then these is approximately 22.1. Killer warms, and now we completely looked every actives, the inductive reactant. Is it close to two pi times the frequency times they looked at? We choose to buy time 60 times, 28 times, 10 to the minus tree. There&#x27;s Emilie there and disease approximately. Dan 0.6 Those and now we have to complicate things. Kidder&#x27;s, which is given by the square root off their existence. A squared plus. The difference between the reactors is squared, and these these equals. True, it&#x27;s square root off 8.8 times. Stand to the third squared plus 22 0.1 time stand to the turd minus 10.6 squared. And these these approximate 23.8 Keeler warms. Now that we have the impudence, we can complicate the current that flows through the circuit. And it&#x27;s given by the voltage divided by the impudence, which is it? Close to 115. Divided by 23.8 times, 10 to the third. And this is approximately four 0.83 merely amperes. Now that we know the current, we can finally calculate what is the voltage across each component of the circuit. So the voltage across the resistance is he goes to the current times, the resistance and these is 4.83 time Stand to the ministry Times 8.8. Time stand The third and Disease 43 vote. Now we can complete the voltage building. Looked her. So the voltage fruiting doctor, it is a quest to the current times they looked reactors and these these equals to 4.83 times 10 to the minus tree times dan 0.6 and these is approximately 0.0 51 votes Now. The voltage across the capacitor is he goes to the current times, the reactive capacitance and these is equals. True, UM, 4.83 time stand to the minus tree times, 22.1 Time stand for the third, and this is approximately 107 votes, which can be further approximated to 0.11 kilo votes.

João Gabriel Alencar Caribé · Answer

to complete the reactors. We only have to remember that I are. A mass is equal to one over the reactor&#x27;s times V are a mess. Then so be for the reactor&#x27;s Get that the reactor&#x27;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&#x27;s on DDE. The initial data given by the problem we have a capacitance that he&#x27;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&#x27;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&#x27;ll be equals to 10 times. They need show every mess current and these easy goes to 5.15 million amperes

Problem

At the measured frequency, what is the ratio of t…

Problem 93 Hard Difficulty

Answer

a) see work
b) 93 $\mathrm{V}$
c) 76 $\mathrm{V}$

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a) see workb) 93 $\mathrm{V}$c) 76 $\mathrm{V}$

Physics

Elyse G.

Andy C.

Zachary M.

Meghan M.

Electric Charge

The Electric Force

James S. WalkerPhysics

Elyse G.

Andy C.

Zachary M.

Meghan M.

a) see work
b) 93 $\mathrm{V}$
c) 76 $\mathrm{V}$

James S. Walker

Physics