ohm meter

More Than You Ever Wanted to Know About Electrical Engineering: Power Transmission Losses

We’ve been talking about step-down transformers that can convert between a high line voltage and more moderate local voltages. You might be asking yourself why we need to do such a thing in the first place. Why can’t we just transmit utility power at 120 V or 240 V?

All right, let’s try it. Say we need to transmit 20 MW of power over a 100 km. If we do it at 240 Vrms, we’ll have a current of 83.3 kArms flowing through the conductor.

Some of the 20 MW we’re transmitting is going to be lost - that is, dissipated as heat. We’d like to minimize losses, so let’s say we’re aiming for 97% efficiency - no more than 3% of that 20 MW lost. Since power dissipated is a function of current and resistance, we know we’ll need a conductor with an overall resistance of 8.64 x 10^-5 Ohms over a distance of 100 km.

The resistance of a conductor is a function of its length, l, its cross-sectional area, A, and the conductor’s resistivity, ρ, which is a property of the material it’s made of. We’ll assume a resistivity here of 8 x 10^-8 Ohm-meters. From here, we can figure out what kind of cross-sectional area our conductor needs - in other words, how large the cable’s diameter has to be.

To make this work, you’d need a conductor with a radius of 5.4 m. Clearly, this isn’t going to happen.

If you want a conductor that’s actually practical, that means you need to transmit power at high voltage - since a higher voltage at the same power will result in a lower current, this means your losses will be lower, allowing you to use a much smaller conductor. Here are the same calculations done with a transmission voltage of 240 kVrms instead of 240 Vrms.

In this case, you need a conductor with a radius of about 0.5 cm, which is much more reasonable.


Updated my Heathkit VTVM (Vacuum tube volt meter). Replaced the 3 old paper capacitors inside with modern equivalents and replaced a pair of resistors with one similar ohm resistor.

This unit it is a model V-1 which is the first VTVM that Heathkit produced, I have no manual or schematic for it and there doesn’t seem to be anything available online. So I really just had to go by the components that were in there already.

I also believe that the unit needs to be calibrated because when I power it on, I cannot zero out the ohm meter and testing a 47ohm resistor just pegs the needle at 0. Might take a look at it a bit today, there are some potentiometers inside that you can adjust. Will have to trace out where they go to try and figure out what they do.