#3. [Simple RC Circuit] The capacitor is initially uncharged, and the switch is open. Then, at time t = 0, the switch is closed. For the following questions: a = 10 V, R = 2000 .0, C = 400 pF [pF = 10'6 F] [a] What is the current in the resistorjust after the switch is closed? Be sure to show your work. (b) What is the final charge on the capacitor after a long time, t > 00. Again, show your work. (c) Sketch graphs showing how each of the labeled voltages below varies with time at, including 1: 0. Label important values [like maximins). Empty graphs are available on the next page. Tip: Notation reminder: Vb\" is the voltage at b from a. For example, in this circuit, Vba = +5, always. (d) When the voltage across the resistor and capacitor are equal in magnitude, what is the fraction of energy stored in the capacitor, vs the final energy stored in the capacitor? Tip: You are finding U/Unal, where U is the energy stored in the capacitor when |VbC| = Weal- (e1 At what time is the voltage across the resistor equal in magnitude to the voltage across the capacitor? Show your work. (f) From 6 = 0 to on, how much total energy is supplied by the battery? Do this two ways: i. By considering the power supplied by the battery, and ii. By considering the power dissipated in the resistor and the energy stored in the capacitor. Please show your work and make sure your reasoning is clear.