Problem

Consider the ac circuit shown in Figure 2436, whe…

05:43

Problem 53 Hard Difficulty

An ac voltmeter, which displays the rms voltage between the
two points touched by its leads, is used to measure voltages in the circuit shown in FIGURE 24-36. In this circuit, the ac generator has
an rms voltage of 9.00 V and a frequency of 25.0 kHz. The inductance in the circuit is 0.250 $\mathrm{mH}$ , the capacitance is 0.150$\mu \mathrm{F}$ , and
the resistance is 2.50$\Omega .$ What is the reading on a voltmeter when
it is connected to points (a) A and B, (b) B and C, (c) A and C, and
(d) A and D?

Answer

a) $88 \mathrm{~V}$
b) $95 V$
c) $7.1 V$
d) 9 $\mathrm{V}$

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Physics 102 Electricity and Magnetism

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Watch More Solved Questions in Chapter 24

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Video Transcript

the voters between the points A and B is given by the following we A B and these will be the R u mass voltage is equals two. The are a mass current that flows from the circle eight times the impudence between points A and B. So now we have to complete two things. I think that's between these two points on the R. M s current. They think that's between the stupid points. A and B is very simple to complete because there is only one doctor between point A and B, so this emptiness between points A and B is equal. Student. The reactor's off that doctor. Sure, the ROMs roses between points A and B. It's given by the R. M s current times inductive reactors. But now we have to complete why using looked reactors And then what is the current we begin by? These are one which is indicative Reactors on these is given by to pi times the frequency times they took turns and these is to pipe times 25 times 10 to the turd times zero point 25 points Stand for the minor street because there is a nearly there and disease approximately 29 point 27 homes. So now we have to complete the R. M s current that flows from all the circuit. And to do that, we have to complete what is the impedance off the complex circuit. So the impudence off the complex circuit is given by the square root off the resistance squared. Plus the difference between the reactant says squared. Then we already know what is inductive reactors. So we have to calculate what is the capacity reactors. And it's getting by. XY is equals to one divided by to pi times the frequency times the capacity us which is one divided by two pi times 25. I'm standing toward times Ah, 0.15 times 10 to the minus six and these is approximately 42 0.44 homes. And now we can help lift impudence. It will be z the coast of the square root off 2.5 squared plus 39.27 minus 42 0.44 squared on disease, approximately 4.0 for homes. So now we can evaluate what is the current that flows from the circuit using the following relation the are a man's voltage is equals to the r. M s current that flows for the circuit times the impedance off that circuit. So they are a mess current easy cause too The voltage invited biting peons And then we have to follow him The voters is he goes to nine votes and impedance is he goes to 4.42 We have that the current that flows from the circle It is approximately two 0.23 amperes and then we can finally complete worries the voltage between points e and B on the circuit. So the volatile between points a unity of the circuit the arguments voltage is it goes to remember the expression the R. M s current 2.23 times the inductive reactors which here's 39 points 27 and then the voltage between points A and B is approximately 88 votes. And now in the second item, we have to complete what is the voltage between points B and C and these is given by the current that flows with a circle. It's times impedance between points being C. But remember that between points BNC, there is only a capacity for so the only contribution to the impedance between points B and C use the reactive capacitance. Then we get that the voters is He goes to the R. M s current times the reactive capacitance which we have already calculated. It was right here. Then the voltage between points BNC is he close to the current that flows for this or quit 2.23 peers times 42.44 homes which is approximately 95 votes. No In the turned item, we have to copulate. What is the voltage between points A and C. So the volatile sweeping points the agency is equals to the R. M s current that flows for the circuit times impedance between points leniency between Point, C and C We have both conductor and the capacitance here. So between points A and C, we have a new doctor on a capacitor. Then the impedance is given by the square root off the difference between the reactors squared and then we keep blinking their values that we have a radical related. So we have the voltage between points. The DNC is equals two two points 23 times the square root off Exhale, which is 39.27 minus exceed, which is 42.44 squared. And these things approximately seven 0.1 votes. Finally, on the last item, we have to complicate what is the voters between points A and E. But note that between points a. Indeed, we have the world circuit that is, between these points and news point. We have the wall circuit. So the voltage difference between points in unity will just be the voltage off the service. So it will be close to nine votes. Our answered for the last item is nine votes straightforwardly.

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