Physics Puzzle: the Bulbs and the Students
Posted on March 26, 2008
Filed Under Physics, Physics Puzzles |
Here’s a nice puzzle to challenge your understanding of simple electricity.
Two students live in adjacent houses in the dorms (ignore the dodgy art, I can only draw as well as Microsoft Word lets me … and yes, the weird beings are the students, courtesy of the Office Clipart). The lightbulbs in their rooms are connected in series. Both students have a physics exam coming up. The students agree to put in 100W lightbulbs. However, they both try to cheat: student A puts in a 50W light bulb, while student B puts in a 200W lightbulb, without informing the other (i.e., neither told the other of what he’d done).
Which student failed the physics exam?
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The 50W and the 200W bulbs will not have these power ratings when used this way, because they will not have the pd across that there made to operate at.
The 50W and the 200W bulb have different resistances
When operating correctly, connected to the same supply voltage,
• the 200W will have a larger current through it (I = P/V);
• hence it must have a smaller resistance (R = V/I)
The same current will flow through each bulb in the set up for this question.
• Hence the bulb with the higher resistance (the 50W) will have the larger pd across it (V = IR)
• and will therefore have the higher power rating (P = IV) in this set up.
So the 200W bulb will shine the less bright and the student B will fail the exam (because he was the dimmer Physicist in both ways).