The 300 μF capacitor in FIGURE P30.75 is initially charged to 100 V, the 1200 μF capacitor is uncharged, and the switches are both open.<IMAGE>

a. What is the maximum voltage to which you can charge the 1200 μF capacitor by the proper closing and opening of the two switches?

Video transcript

Hello, fellow physicists today, we're gonna solve the following practice problem together. So first off, let us read the problem and highlight all the key pieces of information that we need to use in order to solve this problem. A circuit contains two capacitors. The first is a 400 micro ferra capacitor initially charged to 200 volts. While the second is an uncharged 1400 micro Ferra capacitor, both are connected to open switches. What maximum voltage value could be achieved on this uncharged capacitor by correctly operating both switches. So that's our angle. Our angles were trying to figure out what this maximum voltage value is that can be achieved by the specific uncharged capacitor in this particular circuit. And that's our final answer that we're ultimately trying to solve for is what is the maximum voltage value? Awesome. So with that in mind, let's quickly look at our diagram that's provided to us by the prom itself of our circuit. As you can see, starting from the bottom left hand corner, we have our first switch which is called S one and of course it's open and the switch is shown by an arrow and then we have going up, we have our second switch, which is denoted as S two, which is also an arrow pointing to the left that is also open. And then we can see two are on the very top of our circuit. We have two red bars that are parallel to each other denoting our battery which has a voltage of zero volts. And then we have our second capacitor which is gonna be C two, which is 1400 micro for and then going down from the left to the right, going down and in the middle between our first switch and our second switch, we have our inductor L that has a value of 4.9 Henry. And then going down to the very bottom of our circuit, we have another battery that has a voltage V one of 200 volts. And then we have our first capacitor, which is denoted C one which is 400 micro farads. Awesome. So now that we have a visualization of what's going on in this problem, let's look at our multiple choice answers and read them off to see what our file answer might be. And let us note that they're all in the same units of volts. So A is 1.1 multiplied by 10 to the power of two B is 3.2 multiplied by 10 to the power of two C is 4.3 multiplied by 10 to the power of two and D is 5.5 multiplied by 10 to the power of two. OK. Moving right along here, first off, let us write down all of our known variables. So let us know note that C one, our first capacitor is equal to 400 micro Ferras. Let us also know that C two, our second capacitor is equal to 1400 micro ferrets. And let us note that our V one value or voltage for one of our batteries is equal to 200 volts. So now at this point, we need to recall and note that for a two capacitor system, the maximum energy stored inside of the first capacitor will equal the maximum energy stored in the second capacitor. Thus, we should be able to recall and use the phone equation that U one is equal to U two, which means that the energy of the first capacitor is equal to the energy of the second capacitor. Therefore, we can recall and expand this equation to write that one half multiplied by C one multiplied by V one squared is equal to one half multiplied by C two multiplied by V two squared. So now at this point, we need to rearrange this equation to isolate and solve for V two, which is our final answer that we're ultimately trying to solve for which is the maximum voltage that can be achieved. So when we do that, using a little bit of algebra, we will find that V two is equal to V one multiplied by the square root of C one divided by C two. So now at this point, we need to plug in all of our known variables to solve for V two. So when we do, we will find that V two is equal to 200 volt means that our V one value multiplied by the square root of 400 micro faty. That's our C one value divided by our C two value which is 1400 micro ferrets. Awesome. So let me plug that into our calculator. We will get 106.90 volts, which is approximately equal to 1.1 multiplied by 10 to the power of two volts. When we write it in scientific notation and round to one decimal place or rather to be more specific when we round our final answer to two significant figures to match all of our multiple choice answers means all of our multiple choice answers are rounded to two significant figures. And that's it we've solved for this problem. Hooray, we did it. So looking at our multiple choice answers, the correct answer has to be the letter A 1.1 multiplied by 10 to the power of two volts. And that's it we solve for this problem. Thank you so much for watching. Hopefully, that helped and I can't wait to see you in the next video. Bye.