Name one factor that can increase
the electrical resistance of a copper wire at a certain temperature.
Say that we have a wire made of
copper and that this wire has a resistance we can call capital 𝑅. That resistance 𝑅 tells us just
how difficult it is for a charged particle, an electron, to move down the length of
the wire. That resistance happens in large
part because these electrons, as they move along, keep crashing into atoms in the
copper wire. Nonetheless, if all goes well, the
electrons make it across the copper wire.
We want to consider here how we
could increase the resistance of a copper wire, given that it’s fixed at a certain
temperature. If we continue to think in terms of
electrons running into atoms in our current-carrying wire, we start to see there’re
changes we could make to this wire that indeed would make it harder for the
electrons to get from one end to the other. For example, what if we made the
wire longer than it was originally. In this case, a travelling electron
has many more collisions with atoms in this copper material to endure before it
makes it to the end of the wire. In other words, the resistance of
the wire has increased because it’s longer.
But there’s another change we could
make to our copper wire, which would have a similar effect, increasing
resistance. What if, instead of making our wire
longer, we just made it thinner. We decreased its diameter. In this case, there’s simply less
space in the conductor for current to occupy as it travels. To see how this increases
resistance, let’s consider an analogy. Imagine being in a very large field
with lots of people, where each one of these dots represents a person standing in
the field. And imagine further that, at one
end of the field, there’s a wall with a very narrow walkway in the middle of the
wall that people could access.
Imagine what would happen if
everyone in the field decided that they wanted to leave the field and walk down this
narrow walkway. As people moved towards this
walkway, there would be a traffic jam, right. Well, the same thing happens when
we make our wire that carries electrons very narrow. Only a fraction of the electrons
could travel down the wire at any one time. So the resistance of the wire has
effectively gone up. Here’s what we can say then about
factors that increase the electrical resistance of this copper wire. We can increase resistance 𝑅 by
increasing the wire length or decreasing the wire cross-sectional area.
So the length of the wire as well
as its cross-sectional area are both factors that we can change to increase the
electrical resistance of the wire.