From unit 8:
In the course of doing its work, a load will have a voltage drop across it that is proportional to the resistance of that load. Remember E = I * R. You have to keep straight here what this is referring to. For example, if you’re looking at the voltage drop across a load, you would look at
E(voltage drop across the load) = I(current flow through the load) * R(resistance of the load).
If you’re analyzing an entire circuit, you would look at:
E(source or line voltage) = I (total current flow through the circuit) * R(total resistance of ALL the loads in the circuit)
Since you are just wanting to calculate the heat generated at one particular load in a series circuit, you have to use the voltage drop for that load, not the total voltage drop (which of course equals the supply voltage) in the entire circuit, if you use the P = E^2/R equation. It is doable, but not as easy as using the P = I^2 x R equation.