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 five
meters squared. Find the length of the wire. Use 1.7 times 10 to the negative
eight ohm meters for the resistivity of copper. Give your answer to one decimal
place.
We can recall that the resistivity
of a material is given by the following equation, where 𝑅 is the resistance of the
wire, 𝐴 is the cross-sectional area of the wire, and 𝐿 is the length of the
wire. So, if we rearrange this equation,
we can calculate the length of the wire. If we multiply both sides of the
equation by the length 𝐿, then this cancels on the right. If we then divide both sides by the
resistivity ρ, then this cancels on the left. And we find that 𝐿 is equal to 𝑅
times 𝐴 divided by ρ.
We are given values for the
resistance, cross-sectional area, and resistivity. But before we substitute in these
values, we need to make sure that they are in appropriate units. The resistance is given as 12.8
milliohms. So, we need to convert this value
into ohms by dividing by 1000. This will give us 0.0128 ohms. The cross-sectional area is given
as 1.15 times 10 to the negative five meters squared, so the units here are
good. And the resistivity is given as 1.7
times 10 to the negative eight ohm meters, so the units here are good. So, we can now substitute these
values into this equation to calculate the length of the wire.
The length of the wire is given by
0.0128 ohms times 1.15 times 10 to the negative five meters squared divided by 1.7
times 10 to the negative eight ohm meters. Completing this calculation gives
us 8.7 meters to one decimal place. So, the length of the wire is 8.7
meters.
