You and your friend are trying to determine if you can use a capacitor to extend the lives of batteries in circuits. You suggest that you try a simple circuit with a capacitor, originally uncharged, connected to a battery through a switch. To monitor the output energy, you put a light bulb in series with the capacitor. Your friend believes that when the switch is closed the capacitor charges up and the bulb gets brighter and brighter until the brightness levels off. The bulb then stays on until the swit ch is opened. Do you agree? 1.Restate the problem. Do you agree with your friend? If not, describe what you think the behavior of the circuit will be. Give your reasoning. Explain what is going on in each component of the circuit. Sketch a qualitative graph of the bulb's brightness vs. time.