You have a hand-crank generator, and you are tasked with charging up a large 2- Farad capacitor such that it stores 20 coulombs of charge. (You need to put mechanical energy (work) into the generator, and this energy is somehow transferred to the charge; the details of exactly how this transfer happens are not important.)

A) How much energy is stored in the capacitor after you have finished charging it up?

B) Consider adding one coulomb of charge at a time. Which requires more energy from you: the 5th coulomb or the 15th coulomb? Or are they the same? Explain your answer carefully, along the lines of the instructions to Part A of #1.

C) Now, check your answer in part B is consistent with your answer in part A, in the following way. First, calculate the *average* amount of energy needed to add a coulomb of charge. (perhaps comparing the first coulomb and the last coulomb). Then multiply this average by the total number of coulombs added. Show that you get (about) the total energy stored.