1· The circuit at right contains a battery, a bulb, a switch, and a capacitor. T

Question

1· The circuit at right contains a battery, a bulb, a switch, and a capacitor. The capacitor is initally uncharged. Describe the behavior of the bulb in the two situations below. a. Bulb A Battery The switch is first moved to position 1 Describe the behavior of the bulb from just after the switch is closed until a long time later. Explain. i· Capacitor ii. The switch is now moved to position 2. Describe the behavior of the bulb from just afte the switch is closed until a long time later. Explain your reasoning. A second identical bulb is now added to the circuit as shown. The capacitor is discharged. b. Bulb B Bulb C Capacitor i. The switch is now moved to position 1. Describe the behavior of bulbs B and C from just after the switch is closed until a long time later. Explain. Battery How does the initial brightness of bulb C compare to the initial brightness of bulb A in question i of part a? Explain your reasoning. A long time after the switch is closed, is the potential difference across the capacitor crer than, less than, or equal to the potential difference across the battery? Explain.

Explanation / Answer

a) i) when the switch is moved to position 1 (that is closed), the connection is complete with the resistance (bulb) in series. Initially, there is no charge on the capacitor, but when switch 1 is closed, current flows to the capacitor. This results in a build up of positive charge at one of the plates and negative on the other until the potential difference across the capacitor is the same as the potential difference across the battery. In order to flow, the current has to go through the resistor (a bulb in this case). So, we’d see the bulb light for a little bit and then get dimmer and finally go out.

ii) closing switch 2 disconnects the battery from the circuit as switch 1 is now open. In this state, there is just a metal wire that allows the current to flow from one plate of the capacitor to another, again through the resistor (bulb). This will continue until the capacitor returns to neutral. In other words, the capacitor will start discharging. However, there is no solid way of determining a difference in the behavior of the bulb during charging and discharging as the same time constant, RC plays the same role during charging and discharging.

b) i) when switch 1 is closed, the capacitor starts charging but slower as compared to part a. This is because of two bulbs (resistors) which slow down the charging process. Also, the current flowing through bulbs B and C is half of what was flowing through bulb A in part a.Therefore, the bulb lights dimmer but for a longer time and in the end when the capacitor potential deifference is equal to the battery difference, the bulbs go out.

ii) The bulbs look exactly the same during discharge as they did in charging, dimmer than A but lasting longer. At the end the capacitor completely discharges and has zero potential difference.

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