# Losses in wire with varying cross section along its length

Say I have 5 meters of thick wire (10 sqmm), and for the last couple of centimeters, I have to use a piece of 2.5 sqmm wire for mechanical reasons.

When sending a large amount of DC (say, 30 A) through the wire, will the losses / resistance act as if the ENTIRE wire were of the smaller cross section, effectively creating a "bottleneck" and making the remaining 5 meters of 10 sqmm pointless, or is the increase in losses just proportional to the length of the wire with the smaller cross section compared to the length of the wire with the larger one?

IR losses in the cable are proportional to each conductor segment.

Yes - your last few cm of cable does have higher resistance than the other cable segment. You can calculate the loss for each cable segment, then add those losses together to come up with the total loss.

Also be aware that you may need to be concerned with the cable insulation in the smaller-diameter segment. If the current is sufficiently high, the conductor will get hot. The insulation on the conductor must be rated for the temperature that the conductor is operating at.

If the current is too high, the temperature of the smaller-diameter segment will rise to the point where the conductor burns open. You want to ensure that the current is well below that point.

In general, the approach that you are taking is appropriate. Keep the conductor diameter as large as possible right up to the point where it has to get small. The overall loss is minimized when you do this.

I will give you another aspect but very important. Your cable -as you configure- should be protected with a fuse of 16A which is for 2,5mm^2 and NOT with a 35A fuse as it is normal for 10mm^2 (assuming cable is H05V-U type).

This is very basic in electric installations, in order to minimize fire risk.

• Thanks, I'm aware of that. I just wanted to make sure that using a large cross section for most of the cable does actually have the benefit of minimizing losses, even with the short segment of thinner wire. – instinctive Jul 25 '15 at 18:11