Figure E24.14

shows a system of four capacitors, where the potential difference across ab is 50.0 V. (c) How much charge is stored in each of the 10.0-uF and the 9.0-uF capacitors?

Video transcript

Welcome back everybody, We are taking a look at this electronic circuit right here we are told that the capacitance of this first capacitor is 16 micro fare adds, the capacitance of this. Second capacitor is for micro fare adds. The third is eight micro fare adds and the fourth is also eight micro fare adds. Now these are all connected to a battery with a voltage of 100 volts and we are tasked with finding what the charge of Q one or charge of capacitor one and charge of capacitor for our Now before trying to dive into formulas, let's just think about this theoretically here, we see that capacitor ones here in capacitor force here and if you'll notice they are in series, this means that they are going to have the same charge. So we just have to figure what the charge of this entire circuit is and then we will have found the charge of each of the individual capacitors. So the formula for this is going to be the equivalent capacitance of the entire circuit times the voltage of the battery. So we must find the equivalent capacitance first. So let's go ahead and start with these two capacitors that are in parallel because once we find their equivalent capacities then we can just treat it like one capacitor in series with the other two. So the equivalent capacitance of capacitors two and three since they are in parallel, you just add their capacities together. It's just going to be four plus eight giving us 12 micro fare adds. Alright great. So now let's go ahead and move on to the equivalent capacitance. This is going to be equal to, since we are looking at technically three capacitors in series one over the equivalent capacitance will be one over C one plus one over C four plus one over C two three. This is equal to 1/16 plus 1/8 plus 1/12. This gives us an equivalent equivalent capacitance of 3.69 micro fare adds. Great. Now that we have that let's go ahead and calculate our Q one and Q four, they equal the same thing. It'll just be ce que times our voltage which is 3.69 micro fare adds times 100 volts, gives us 369 micro columns corresponding to our final answer choice of C. Thank you all so much for watching. Hope this video helped. We will see you all in the next one.