We'll Share The Bill
Tom and Harry are roommates whose ceiling lights are connected in a series circuit. They agreed to each install a bulb in their rooms, and split the electricity bill equally.
However, Tom decides to get more light at Harry’s expense. Thinking that a higher wattage bulb is better, Tom installed a bulb. Harry being fair, installed a bulb.
Will Tom succeed in cheating Harry?
Details and Assumptions:
- Both the bulbs have equal voltage ratings.
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1 solution
The wattage rating of a light bulb is inversely proportional to its resistance. If both had used 100 watt bulbs, the total resistance would double, therefore it would consume 50 watts total, split evenly, so each bulb would consume 25 watts.
By substitute in a 200 watt bulb, the total resistance is 1.5 times that of a single 100 watt bulb, making the total consumption ~66 watts, but the voltage drop will be twice as high across the bulb with greater resistance (the 100 watt bulb) resulting in a 2:1 split of wattage, with the 100 watt bulb consuming ~44 watts and the 200 watt bulb consuming ~22 watts. Oops!