### Video Transcript

A copper wire with a resistance of
12.8 milliohms has a cross-sectional area of 1.15 times 10 to the negative fifth
meter squared. Find the length of the wire. Use 1.7 times 10 to the negative
eighth ohms times meters for the resistivity of copper.

Let’s begin by drawing a diagram of
our copper wire. In our diagram, we’ve labeled our
copper wire with a resistivity 𝜌 of 1.7 times 10 to the negative eighth ohm meters,
a cross-sectional area 𝐴 of 1.15 times 10 to the negative fifth meter squared, a
resistance 𝑅 of 12.8 milliohms, and we are solving for the length of the wire
𝐿.

Before we do any calculations, we
need to recall an equation that relates the resistivity, cross-sectional area,
length, and resistance of our wire to each other. That equation is 𝑅, the resistance
of the wire, is equal to 𝜌, the resistivity of the wire, times 𝐿, the length of
the wire, divided by 𝐴, the cross-sectional area of the wire. The problem asked us to solve for
the length of the wire. Therefore, we must rearrange our
formula so that we are solving for 𝐿.

To do this, we have to multiply
both sides of the equation by 𝐴 over 𝜌. This will cancel out both the 𝐴
and the 𝜌 on the right side of the equation, leaving us with the relationship 𝐴
times 𝑅 divided by 𝜌 is equal to 𝐿. We can now substitute in our values
for our variables. For our area, we use 1.15 times 10
to the negative fifth meter squared. The resistance is 12.8
milliohms. And the resistivity is 1.7 times 10
to the negative eighth ohms meters.

We need to be careful with our
units. Our resistance is given to us in
milliohms, but it needs to be converted into ohms. We need to remember that milli- is
the prefix for 10 to the negative third. Therefore, we can replace 12.8
milliohms with 12.8 times 10 to the negative third ohms. When we multiply out our fraction,
we get a length of the wire as 8.66 meters. The resistivity in our problem was
given to two significant figures. Therefore, we must report back our
length to two significant figures. 8.66 meters rounds to 8.7
meters. The length of the wire is 8.7
meters.