Power consumed by an electrical load I saw this quote on a website recently:

"A fundamental law of electric circuits is, that because current must be constant all the way around a circuit, only half the power of a generator can be consumed by the load. Every time you make some toast, an equal amount of heat must be dissipated at the power station and along the power lines."

Is this true?  I don't think it is.  I think it may be somewhat true, but I think something is being missed.  For one, I can agree that the current in the circuit needs to stay the same, but if the load depletes a large amount of the voltage, then you could have very low power on the return leg.
 A: Not true. What is true that during maximum power transfer, and only for maximum power transfer, the dissipated power is equal to the power dissipated in the source impedance. The amount of power that can be dissipated in a load depends on the source impedance. For example, take the simplest dc case with a battery voltage $V_B$ and internal resistance $R_B$ loaded with $R_L$. The current is $I_L=I_B=\frac{V_B}{R_B+R_L}$ and the power dissipated in the load is then $$P_L=I_L^2R_B=\left(\frac{V_B}{R_B+R_L}\right)^2R_L\\
=V_B^2\frac{R_L}{(R_B+R_L)^2}.$$
Meanwhile the battery's internal dissipation is
$$P_B=I_L^2R_B=\left(\frac{V_B}{R_B+R_L}\right)^2R_B\\
=V_B^2 \frac{R_B}{(R_B+R_L)^2}.$$
Now add them the two dissipations you get $$P_B+P_L=V_B^2 \frac{R_B}{(R_B+R_L)^2}+V_B^2 \frac{R_L}{(R_B+R_L)^2}\\
=V_B^2 \frac{1}{R_B+R_L}=V_BI_B$$
which is the total power the battery provides at any given time. The ratio of the two powers, dissipated in the load and dissipated in the battery internally is of course $\frac{P_L}{P_B}=\frac{R_L}{R_B}$ and the two powers are equal when the load resistance equals the internal resistance, otherwise not.
For a fixed $R_B$ and $V_B$ it is easy to show that $P_L=V_B^2\frac{R_L}{(R_B+R_L)^2}$ is a maximum for $R_L=R_B$.
RF engineers always try to do this at the final stages of their amplifier tuned circuits but low frequency power delivery systems almost never. The reason for this lies in the very different natures of the power generating devices and loads, for examples antennas vs. an oven, and the behavior of transmission lines that are short v. long where length is measured in wavelength.
