Difference in Brightness between Two Bulbs

AI Thread Summary
When two lightbulbs with different resistances are connected in series, the bulb with the higher resistance (R2) is brighter due to the power equation P=I^2R. Conversely, when connected in parallel, the bulb with the lower resistance (R1) is brighter, as indicated by P=V^2/R. The key distinction lies in the fact that current (I) is the same in series, while voltage (V) is the same in parallel. Understanding which variable remains constant in each configuration is crucial for applying the correct power equation. This clarification aids in determining brightness based on the arrangement of the bulbs.
crastinus
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Homework Statement


Two lightbulbs of resistance R1 and R2 (R2 > R1) are connected in series. Which is brighter? What if they are connected in parallel? Explain.

Homework Equations


P=V^2/R
P=I^2R

The Attempt at a Solution


I know the solution.

In series, P1=I^2R1 < P2=I^2R2, so R2 is brighter.

In parallel, P1=V^2/R1 > P2=V^2/R2; since R2 > R1, R1 is brighter here.

But my question is this: How can I know which equation to use for series and which for parallel? (The text says nothing.)

Why couldn't I have argued in the following way?

In paralle, P1=I^2R1 < P2=I^2R2, so, even in parallel, R2 is brighter. Why does this line of reasoning fail?

My best answer is this:

I is different in each case because they are connected in parallel. So, we can't use P=I^2R for this part; we have to find an equation for which another variable is the same. Best bet is P=V^2/R. Even if that's right, I still don't think I really have grasped the relevant issues here.

Thanks.
 
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crastinus said:
How can I know which equation to use for series and which for parallel?
Hi crastinus:

In series what is the same for both R1 and R2?
In parallel what is the same for both R1 and R2?

Hope this helps.

Regards,
Buzz
 
Thanks, Buzz! That helped!
 
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