Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

$\bullet$ Five voltmeters, calibrated to read rms values, are connected as shown in Figure $22.22 .$ Let $R=200 \Omega, L=0.400 \mathrm{H}$ and $C=6.00 \mu \mathrm{F}$ . The source voltage amplitude is $V=30.0 \mathrm{V}$ What is the reading of each voltmeter if $($ a) $\omega=200 \mathrm{rad} / \mathrm{s}$ (b) $\omega=1000 \mathrm{rad} / \mathrm{s} ?$

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

a) 21.21 $\mathrm{V}$b) 21.2 $\mathrm{V}$

Physics 102 Electricity and Magnetism

Chapter 22

Alternating Current

Current, Resistance, and Electromotive Force

Direct-Current Circuits

Electromagnetic Induction

University of Washington

Simon Fraser University

Hope College

University of Sheffield

Lectures

04:44

Alternating current (AC) is an electric current which periodically reverses direction, in contrast to direct current (DC) which flows only in one direction. Alternating current is the form in which electric power is delivered to businesses and residences, and it is the form of electrical energy that consumers typically use when they plug electrical appliances into a wall socket. A common source of DC power is a battery cell in a flashlight. The abbreviations AC and DC are often used to mean simply alternating and direct, as when they modify current or voltage.

11:31

In electrical engineering, a direct current (DC) circuit is an electrical circuit operating with a constant voltage (or current), as opposed to alternating current (AC) circuits. Direct current may flow in a conductor such as a wire, but can also flow through semiconductors, insulators, or even through a vacuum as in electron or ion beams.

09:01

Five infinite-impedance vo…

10:04

12:35

04:58

(III) $(a)$ What is the rm…

05:03

(III) ($a$) What is the rm…

07:16

An ac voltmeter, which dis…

02:40

(III) A $120-\mathrm{V}$ r…

05:23

Point $a$ in Fig. $\mathbf…

we have some givens. We have the resistance of the resistor 200 arms. We have the inducting ts of Thean Doctor 0.400 Henry's. We have the capacitance at six. Micro fared so 6.0 times 10 to the negative sixth parents and we have the maximum voltage and this is at 30 0.0 VOCs and we have five years. So given the figure in 22.22 we have four part ay at the arrest. At a angular frequency of 200 radiance per second, we have the inductive reactant equaling Omega Times. The induct into this would be equaling 2 200 ratings per second, multiplied by 0.4 100 Henry's and the inductive reactant CE is given 80 arms the capacitive reactive XYZ, then equaling one over Omega Psi. This would be equaling 21 over 200 radiance per second, multiplied by the capacitance of 6.0 times 10 to the negative six carats, and we find that the capacitive react Ince's equaling two, 833.33 homes. Now we can solve for the impotence the impotence Z equaling the square root of R squared plus the inductive reactant CE minus the capacity of reactant ce quantity. Squared Z would then be able to the square root of 200 hums quantity squared plus 80 minus 833.33 quantity squared. I'm square and we find that tansy is equaling. Two, 779.43 arms. This would be the impotence the maximum current is given as the maximum voltage divided by Z, the impotence and we can solve For the maximum period. This would be equaling to the maximum voltage of 30.0 votes divided by the impotence of 779.43 thumbs. And this is giving 3 38.49 milli amps. The R. M s current is given as the maximum current divided by radical too. And this is gonna be 38.49 milli amps. We can keep it in millions because the denominator is you, Nicolas, and this is giving us 27.22 millions. Now. The reading of each volt meter now should be and this is again according to figure, 22.22 Devi sub one is going to be the R. M s current multiple multiplied by the resistance of the resistor. So this would be pulling 2 27.2 two times 10 to the negative third amps multiplied by 200 arms. And this is giving us 5.44 volts. These two would be equaling to the R. M s current multiplied by the inductive reactant. So this would be going to again 27.22 times 10 to the negative. Ah, third amps multiplied by here, 80 arms and this is giving us 2.17 bolts. Visa three then is gonna is giving us the arm s current multiplied by the capacitive reactant CE. And in this case, 27.22 times 10 to the night of third amps multiplied by 833.3 three homes. And this is giving us 22.68 votes. So this would be your three answers for the three bolt meters. Now we know that Volt meter four would simply be equal to vote Mir three. My has told me to, and this would be equaling 2 22.68 minus 2.17 giving us 20 0.5 one votes, and we know that we'll meet her. Five would be giving us the square root of a volt meter, four squared plus volt meter, one squared so this would be equal in a square root. Uh, 20.50 boats squared plus 5.44 provokes squared. Extend the square root, and this is a decent five would be equaling 21.21 bolts. So these five answers would be, of course, you're five volt meter readings for part A. Now at part B. We're doing the exact same thing, except now we have a different angular frequency, so we have then Omega equaling 1000 radiance per second. And for calculations sake, it's better simply to write 10 to the third. And so the inductive reactant ce we know is Omega multiplied by Al. This would be again 10 to the third. I'll lose the units simply for space multiplied by 0.400 Henry's, and this is giving us 400 homes the capacitive reactor, Ince's again one over Omega Psi. And this is gonna be equaling two, 166.67 arms. So now the inductive reactant is greater the than the capacitive reactant ce, and we can find the impotency. This would be equaling to the square root of r squared again, plus the difference between the inductive reactant ce minus the capacitive reactor. It's quantity squared and this is giving us 307.32 bums again, The calculations are the exact same except that the angular frequency is simply changed too tense that their tents of third radiance per second moving on to the maximum current. This is again the maximum voltage divided by the impotence giving us 97.6 million amps. The are a mess current simply the maximum current reduced by a factor of radical too, giving us approximately 69 million amps. And so going to the readings of the vote meters. Now we can say that visa of one will be equaling. Two are and s wants Bye bye are in this case This would be 69 times 10 to the negative third amps multiplied by 200 arms giving us 13.8 volts. These of two is going to be the r. M s current multiplied by the inductive reactant CE. This is again 69 times 10 to the negative third amps multiplied by 400 homes. And this is giving us 27.6 volts Bees of three equaling the R. M s current multiplied by the capacitive reactor. It's giving us 11.5 volts the sub four, of course, giving us visa to minus Visa three. 27.6 minus 11.5. Visa four is giving us 16.1 volts and quickly for Visa five. This would be the square root of dese of one squared plus visa before squared. Visa five, giving us 21 0.2 votes. These would be our five answers for part B. That is the end of the solution. Thank you for watching

View More Answers From This Book

Find Another Textbook

03:44

The weight of high school kids have been found to have a mean of100 poun…