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$\bullet$ The voltage amplitude of an ac source is $25.0 \mathrm{V},$ and itsangular frequency is 1000 $\mathrm{rad} / \mathrm{s} .$ Find the current amplitude ifthe capacitance of a capacitor connected across the source is (a) $0.0100 \mu \mathrm{F},(\mathrm{b}) 1.00 \mu \mathrm{F},(\mathrm{c}) 100 \mu \mathrm{F}$

a) 0.259$m A$b) 25 $\mathrm{m} \mathrm{A}$c) 2.5 $\mathrm{A}$

Physics 102 Electricity and Magnetism

Chapter 22

Alternating Current

Current, Resistance, and Electromotive Force

Direct-Current Circuits

Electromagnetic Induction

Simon Fraser University

Hope College

University of Winnipeg

McMaster University

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So you know, the voltage V is equal in 25.0 votes. We know that omega, that angular frequency is equaling 10 to the third ratings for second or 1000 radiance for second. And so for party, the capacitance see is equaling 0.0 100 micro fares. We can then say that the voltages equaling the current multiplied by the capacity of reactions. This would be equal into the current, divided by the natural by the angular frequency multiplied by the craftsman's. And so we can solve. For the current I. This would be equaling to the voltage multiplied by the angular frequency multiplied by the capacitance. So this would be 25.0 votes multiplied by tend to the third radiance per second multiplied by. So, you know, the voltage V is equal in 25.0 votes. We know that omega that angular frequency is equaling 10 to the third ratings for second or 1000 radiance for second. And so for party, the capacitance seat is equaling 0.0 100 micro fares. We can then say that the voltages equaling the current 0.100 times 10 to the negative sixth fairs and we have that I is gonna be equaling two 0.250 millions. Or we can simply say 2.50 times 10 to the negative fourth amps. Moving on to part B. We have a capacitance equaling multiplied by the capacity of reactions. This would be equal into the current, divided by the natural by the angular frequency multiplied by the craftsman's. And so we can solve. For the current I, this would be equaling to the voltage multiplied by the angular frequency multiplied by the capacitance. So this would be 25.0 votes multiplied by 10 to the third radiance per second, multiplied by a point one ferret, one microt fared rather. And as you can see, this is simply 100 times our answer from part, eh? And we can see that the current is directly proportional to the capacitance. So if the capacitance is raised by is increased by a factor of 100 while all other variables remain the same, we can say that then the current will simply be equal to 100 times our value from part ay, so point to fuck. Uh, 2.50 times 10 tint 0100 times 10 to the negative sixth fairs. And we have that I is gonna be equaling two 0.250 millions. Or we can simply say 2.50 times 10 to the negative fourth amps. Moving on to part B. We have a capacitance equaling made 1/4 amps. Becomes 2.50 times 10 to the negative second camps. For part C, the capacitance is 100 micro fairs. And again, this is ah, be capacitance from part be raised by a factor of 100. Therefore, our current will also be raised by a factor of 100. Given that, uh, the current one ferret one microt fared rather. And as you can see, this is simply 100 times our answer from part, eh? And we can see that the current is directly proportional to the capacitance. So if the capacitance is raised by is increased by a factor of 100 while all other variables remain the same, we can say that then the current will simply be equal to 100 times our value from part. Eh? So point to fuck 2.50 times temperament is directly proportional to the past sins and all other American l other variables remain the same. So we have the current in part, see equaling than 2.50 amps. That is the end of the solution. Thank you for watching.

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