1. The problem statement, all variables and given/known data Not homework but this seems the best place to post this. In a private conversation someone posted this explanation from a book on how a lamp filament fails.. I'm having some trouble doing the maths to show that the thinner higher resistance part gets hotter... 2. Relevant equations Ohms law 3. The attempt at a solution Imagine the filament is made up of two resistors in series R1 and R2 (See diagram). Let R2 be the part that's getting thinner for some reason... The voltage on R2 is given by the potential divider rule.. VR2 = V * R2/(R1+R2) The power dissipated in R2 is WR2 = (V * R2/(R1+R2)2/R2 If you expand and simplify you get.. WR2 = (V2 * R2) / (R12 + 2R1R2 + R22) So if R2 increases the power in R2 decreases due to the R22. That should reduce the temperature in R2 which is the opposite of what the book suggests. Have I made an error?