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The maximum current in a $22-\mu \mathrm{F}$ capacitor connected to anac generator with a frequency of 120 $\mathrm{Hz}$ is 0.15 $\mathrm{A}$ . (a) What is the maximum voltage of the generator? (b) What is the voltage acrossthe capacitor when the current in the circuit is 0.10 A and increas-ing? (c) What is the voltage across the capacitor when the currentin the circuit is 0.10 A and decreasing?

a) 9.0 $\mathrm{V}$b) $-6.7 \mathrm{V}$c) 6.7 $\mathrm{V}$

Physics 102 Electricity and Magnetism

Chapter 24

Alternating-Current Circuits

Current, Resistance, and Electromotive Force

Direct-Current Circuits

Electromagnetic Induction

Alternating Current

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to conflict the maximum voltage. We only have to use the following relation between the maximum current and the maximum voltage. So their relation is the following the maximum current. Is it close to to pie times the frequency times the capacitance times the maximum voltage solving for the maximum voltage we get that the marks is equals True I max divided by troop i times the frequency times, the capacitance plugging in the given values they get that the maximum voltage is he goes to 0.15 divided by troop I times 120 times 22 times Stand for the mind of six which is approximately in close to nine votes To begin the second item We remember that the current is given by the maximum current times the sign off some phase That depends on the time I noticed that it will not be relevant to us. What is the form off the time dependents? So we just write it as the maximum current time to this sign off that face And no, we say that the current right now is equals to 0.1 and peers so 0.1 Is he goes to the maximum current 0.15 times the sign off that phase. We don't we get that this sign off that phase is equals to 0.1, divided by 0.15 and these is equals. True, true, over free. With that result, we can complete the co sign off that faith by using the falling relation. The science squared off Dita plus the co sign Squared off detail is It goes to one so the cool sign off Tita is equals two plus or minus the square it off. One mine's the sine squared off detail. Therefore, in our case, the coastline of teeter is it goes to plus or minus the square. Root off one miners for over nine and eases equals two plus or minus the square root off five overnight. And this is important because the voltage across the capacitor at any instant of time is equal to the maximum voltage times miners the cool sign off that phase. So now we have to decide whether we will use the positive solution off the coastline or the negative solution off the coastline. And these depends on that increasing or decreasing information and to decide we take a look at the phase or diagram from the situation. So the phase or diagram is as follows we have in these axes current and in that axis, the voltage. So in this, in this situation, off this item here, the current is he goes to 0.1 em peers and it is increasing. So our face vector, you're somewhere in these section off the plane. So disease, our phase and that phase will increase as time goes by and you will make the value off the current increase too. And in this sector here for these value off the things we have to choose the positive solution for the call sign. Therefore, for the second item, the voltage is he goes to minus nine times the square root off five over nine, which is approximately 6.7 minus 6.7 votes similarly on the situation off items. See, we have that the current is it goes to 0.1 and decreasing. In that case, the case off the situation off the item c. Our phaser is somewhere in these regions off the plane. So these ease our face now, notice that as the time passes the phase of actor we will rotate on the current will decrease. But at this time we have to use the negative solution off the coastline because we are on the region where the coast signs are negative and therefore we have that the voltage is equals two minus nine times minus the square root off five overnight, which is approximately 6.7 votes.

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