A heater rated to dissipate power P is run from a fixed supply. If its resistance R is halved (voltage unchanged), the power it dissipates becomes

1. At fixed voltage V, use $P = V^2/R$. 2. So at constant V, power is inversely proportional to R. 3. Halving R doubles the power: new power $= 2P$. 4. Using $P = I^2 R$ here is a trap because I changes when R changes; P/4 and P/2 misapply that form. _Source: syllabus Physics Ch 3 "Current Electricity", p.12_