Problem

Charging and discharging a capacitor. An initiall…

14:38

Problem 70 Hard Difficulty

Charging and discharging a capacitor. A 1.50$\mu \mathrm{F}$ capacitor is charged through a 125$\Omega$ resistor and then discharged through the same resistor by short-circuiting the battery. While the capacitor is being charged, find (a) the time for the charge on its plates to reach $1-1 / e$ of its maximum value and (b) the current in the circuit at that time. (c) During the discharge of the capacitor, find the time for the charge on its plates to decrease to 1/e of its initial value. Also, find the time for the current in the circuit to decrease to 1$/ e$ of its initial value.

Answer

a. the required time to reach the maximum charge on the capacitor is $[86.1 \mu \mathrm{s}]$
b. the current in the circuit is $\left(0.633) I_{0}\right$
c. the time taken for the current in the circuit decreases to 1$/ e$ of its initial value is $188 \mu s$

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Physics 102 Electricity and Magnetism

College Physics

Chapter 19

Current, Resistance, and Direct-Current Circuit

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Video Transcript

in this question were given an RC savior with resistance 135 home and capacitance 15 Michael which is 1.5. I'M stand by my six fatty. I'm sorry. It's micro fatter. Yes. Now. So obviously that I'm constant in this case is RC which is 1 25 and 1.5 cent. Apartment six, which is 0.88 music now this Now that you know this, let's go. Bye. In this question, the capacitor is charging. So we have a sister on the capacitor and they're connected to our batteries farces. I know the capacitor is charging. We know that the master is charging up the charge cause us you're not times one minus minus. Steve, I tell Thank you. Not is the final charge in maximum charge after a really long time. So do you want has given the question? We want to find out when the charge will be one minus one. By e times the maximum charge. So we want our charge to be one minus one by he was the maximum charge. So using these two equations equating these two we get, you know, dance one minus four minus t vital if you call the Cunard into one minus one by so we can see you're not every day 51 toget to get us. If I minded, Steve is one by which is minus one. Now, if you can see this, we can see that because the exponents must be seen. Which means he wiped out his one, which means Tiesto. And this happens after one that one time constant or B. You want to find out what the current will be? This phone. You know that What for charging capacitor. I goes us. I not even dynasty by Tel, that is it. Start off starts off with a maximum value on exponentially decreases as the charge as the capacitor getting starch. And when these evil hotel as we just saw I do not I'm skip are minus one That is I not buy it. Hence it falls after one. Thank you. After one constant, the current is won by e times the maximum current Just settle on 368 times the maximum current. Now for the next part we want to consider the case Window capacitor is discharging. So we have the your sister and we have the capacitor on nothing else in the secure and the kid Faster has some charge on So in this case for park Si we want to find out who ended it Charge will be one by e times the maximum charge. We know that for a discharging capacitor the charge expanding exponentially d case that is at any time he touched you will be the maximum charge I'm even dynasty white out hence using these two equations we write you know by E is equal to you not even dynasty right out Excuse us If our dynasty by tell is even minus one it means he is a good hotel The same as the last question It happens after one time constant within boxy we all want also want to find out when the current will be maximum current times one by now for discharging capacitor You bastard! You know that the current again d case as if our dynasty wayto Because as the charge gets defused, the pastor's world which falls and the current also falls. And even in this case, using these three questions you see I not evil dynasty right help is not equal minus one, which means he's able to tell which is the same for all four questions

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