### Video Transcript

Three capacitors, with capacitances of ๐ถ one equals 1.5 microfarads, ๐ถ two equals 5.0 microfarads, and ๐ถ three equals 8.0 microfarads, are connected in parallel. A 720-volt potential difference is applied across the combination. What is the voltage across the ๐ถ one capacitor? What is the charge across the ๐ถ two capacitor?

Weโre told here that these three capacitors are connected in parallel and that they have a potential difference power supply. We may as well go ahead and draw this as a circuit. So here, we have it: capacitors ๐ถ one, ๐ถ two, and ๐ถ three are arranged in parallel in the circuit with a 720-volt potential difference across it.

In our first question, weโre asked to solve for the voltage across the ๐ถ one capacitor, where the values for ๐ถ one, ๐ถ two, and ๐ถ three are all given to us in the problem statement. Interestingly though, for this particular question, we wonโt need to know the value of the ๐ถ one capacitor. To see why, letโs consider this circuit that weโve drawn.

We know that 720 volts of potential difference is set up across the positive and negative terminals of our cell. Furthermore, in this idealized circuit, the only elements that use up that potential difference are the capacitors ๐ถ one, ๐ถ two, and ๐ถ three. And since they are arranged in parallel, that means the voltage drop across any one of our three capacitors must be equal to the total voltage supplied to the circuit.

There is nowhere else for voltage to drop in the circuit. And so that tells us the answer to this first question. The voltage drop across the ๐ถ one capacitor โ weโll call it ๐ sub ๐ถ one โ is equal to 720 volts, the same for ๐ถ two and ๐ถ three by the way.

Letโs now move on to part two, which asks not for the voltage, but the charge across the ๐ถ two capacitor. To figure out what this charge is, letโs recall a relationship between charge, capacitance, and potential difference.

The capacitance ๐ถ of a capacitor is equal to the charge on the plates divided by the potential difference across them. Applying this relationship to our scenario, we can say ๐ two โ the charge across the ๐ถ two capacitor โ is equal to that capacitance times the potential across the capacitor.

Now remember we saw in part one that 720 volts is yes, the potential difference across ๐ถ one, but itโs also the potential difference across the other capacitors. That takes care of ๐ sub ๐ถ two. And then, for ๐ถ two, the capacitance value itself, thatโs told to us in the problem statement; itโs 5.0 microfarads.

When we plug in and then multiply these two terms together, we find a result of 3.6 millicoulombs. Thatโs the amount of charge across the ๐ถ two capacitor.