A parallel-plate air capacitor has a capacitance of 920 pF. The c...

Question

A parallel-plate air capacitor has a capacitance of 920 pF. The charge on each plate is 3.90 uC. (a) What is the potential difference between the plates? (b) If the charge is kept constant, what will be the potential difference if the plate separation is doubled? (c) How much work is required to double the separation?

Accepted Answer

Welcome back everybody. We are making observations about a device that consists of two identical capacitors. We are told that the capacitance on each one is 430 PICO fair ads or 430 times 10 to the negative 12 fair ads. We're told that the charge on each of the plates is 1.45 micro columns or 1.45 times 10 to the negative six columns. And we are tasked with finding a couple different things here. A We are tasked with finding what is the voltage difference across the plates. Be? What will be the new voltage difference when we triple the distance that they are currently at. Which by the way, we're not told that. So we're just going to say their current distance is just equal to D. And then see we are tasked with finding what is the work done by tripling the separation here. So let's go ahead and start out with part a part is pretty easy. We're just gonna use this formula here that the voltage difference is simply just the maximum charge divided by the capacitance. So we have that this is 1.45 times to the negative six, divided by 430 times 10 to the negative 12. This is equal to my apologies. This is equal to 3.37 times 10 to the 3rd. 4. Our voltage difference. No, we are now going to take the metal plates here and separate them by triple the distance at what they were at. And now we need to find what the new voltage difference is. Well, the charge, the maximum charge is gonna stay the same. But now there's going to be a new capacitance and here's why we have that are capacitance is equal to epsilon. Not times the surface area divided by the distance. But now we are going to triple the distance. Right? So now we are going to go to epsilon not times the area uh divided by three times the original distance, which really, if you think about it, is just the original capacitance divided by three. This is our new capacitance. So let's plug this into our equation right here. And I'm actually just going to scroll down just a little bit. So we have that our new voltage distance is equal to you divided by C. Divided by three A K A three times Q over C. Well, we already calculated our, our old voltage here. So it's just going to be three times 3.37 times 10 to the third. Giving us a new voltage difference of 1. times 10 to the fourth vaults. Great. So now let's go ahead and move on to part C. Here. We need to figure out the work done by tripling the separation between the two plates. Well, the work done is just going to be the change in the internal energy stored. A K. You're going to have your final energy stored minus your initial energy stored. But what exactly is that going to be? Well let's look at the formulas just for the stored energy here, our initial stored energy will just be the maximum charge squared divided by two times the capacitance. Our final stored energy is going to be Q squared divided by two times the new capacitance. Well we know that the new capacitance is just C divided by three. So we're gonna have the same thing. We're gonna have three times U squared divided by two C. Which is just three times the initial stored energy. So now just scrolling down just a little bit more here we have that the work done is equal to three U. I minus you. I this is equal to two times our initial energy stored. So let's go ahead and calculate that we have two times two Q squared all over to see and we can plug in all of these numbers. So we have two times 1.45 times 10 to the negative six. Where'd all over? Two times 430 times 10 to the negative 12. Giving us a final answer of 4.89 times 10 to the negative third jewels. So now we have found the original voltage. The new voltage difference in the work done by making that separation which corresponds to our final answer choice of the Thank you all so much for watching. Hope this video helped. We will see you all in the next one

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