[a common misconception with a series rc circuit with battery is that the capacitor is eventually "fully charged". a capacitor can always be charged more if the voltage is increased. this problem should you think about the relationship of the charge on the capacitor and the rest of the circuit. it is also a great exercise of differential equations since you can repurpose the knowledge of the one you know, even though the situation is different. ] a physics graduate student builds the circuit below, with a switch allowing the circuit to close with either battery: (a) first, the graduate student flips the switch to b, connecting the 28 battery. assuming the capacitor starts uncharged, what will its charge go to if she waits a very long time? (b) after waiting a long time, the graduate student declares it to be t = 0 and flips the switch from b to a, connecting the & battery. find q (t) by using kirchhoff's rules to get a differential equation and then plugging in the solution to that equation. (hint: what direction does current flow? ) (c) check the t → 0 and t → oo limits of your answer, and plot q as a function of time. does your answer make sense