3. A light bulb is connected in the circuit shown below -- the switch S is initially open and the capacitor is is uncharged. The battery has no appreciable internal resistance and a voltage = 12V. The resistance of the light bulb is 1000 0, R = 500 and C = 100pF . The switch is closed at t=0. Bulb a) Find the all of the currents at t=0+. b) Find all of the currents after a very long time. c) Find the current in the bulb as a function of time. d) Sketch the brightness of the bulb as a function of time