# High voltage in electric power transmission systems - why Ohm law is used regardless of "assuming the power is completely converted into heat"?

Similar questions feature found about 10 QA's here on the subject with all about 1-5 cumulative upvotes. For example Why do power lines use high voltage? have 6 upvotes for accepted answer:

The line loss is given by $$P_{loss}=I^2R$$, or, substituting for $$I$$, $$P_{loss} = \frac {P^2R}{V^2}$$

However in wiki Joule_heating there is an assumption for using that formula:

Assuming the element behaves as a perfect resistor and that the power is completely converted into heat, the formula can be re-written by substituting Ohm's law

Why is Ohm law applied in many answers and articles explaining the reason for high voltage when it is applicable for complete conversion of energy (but losses are less than 100% in mains power)? or wiki incorrectly adds this condition?

P.S. the answer quoted above is actually much better than a place from where I started my "quest", those as far as I recall just stated voltage is stepped up because losses are square of current; but (if Ohm law is applied) losses are also square of voltage $$P_{loss}=I^2R=V^2/R$$ so I wanted better explanation and started web search and read wiki, but (at least wiki Joule_heating page) on the subject stated only:

However, in applications where heating is an unwanted by-product of current use (e.g., load losses in electrical transformers) the diversion of energy is often referred to as resistive loss. The use of high voltages in electric power transmission systems is specifically designed to reduce such losses in cabling by operating with commensurately lower currents.

Why is Ohm law applied in many answers and articles explaining the reason for high voltage when it is applicable for complete conversion of energy (but losses are less than 100% in mains power)? or wiki incorrectly adds this condition?

The Wikipedia article on Joule heating is not incorrect in adding that condition.

In the case of power distribution line losses, Ohm’s law isn’t 100% accurate, but it is a very good approximation. The majority of the power lost in a power distribution line can be represented by Ohm’s law, even if it isn’t exactly 100%. So for power distribution it is a useful approximation, and captures the basis of the design decision to use high voltage transmission lines.

Now, you may be thinking of the power dissipated in the load, but that is not of interest in the decision to use high voltage transmission lines. All that is of interest there is the losses in the distribution lines themselves. From the perspective of the power company, power dissipated in the load is revenue but power dissipated in the lines is cost. They are trying to minimize costs, not minimize revenue.

• thank you. I like Wiki and I would want to edit/fix. could you please explain more so that edit is justified. Nov 26, 2021 at 0:10
• I don’t think it needs to be fixed. It is ok as it is
– Dale
Nov 26, 2021 at 1:11
• "The Wikipedia article on Joule heating is not incorrect in adding that condition." - what did you mean than? Nov 26, 2021 at 9:06
• @Martian2020 I meant what I said: that I thought it was not incorrect. If it were incorrect then it should be corrected. Since it is not incorrect it does not need to be corrected.
– Dale
Nov 26, 2021 at 12:22
• thank you, was too many not for me to see at once. Nov 26, 2021 at 13:55