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Why resistance increases with length of wire

A shallower potential gradient or 'voltage slope'

Try Why Do Astronauts Float by Julian Hamm

Imagine two lengths of wire, one 12 cm long the other 6 cm long.  Let's connect them both across 6 V.

You can imagine the potential dropping evenly from one end of the wire to the other.  6 V at one end. 3 V in the middle.  0 V at the other end.

For the shorter wire each cm of wire has 1 V across it.  For the longer one each cm of wire only has 0.5 V across it.  So the current through the longer wire is half the current through the shorter one because there's only half the voltage across each centimetre.

This idea of volts per centimeter is called the potential gradient.  Longer wires have a shallower potential gradient along them than short wires.  This is why we say their resistance is higher.

back to Lesson 7: Resistance and Ohm's Law