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