Video Transcript
A wire made of an unknown substance
has a resistance of 125 milliohms. The wire has a length of 1.8 meters
and a cross-sectional area of 2.35 times 10 to the negative five meters squared. What is the resistivity of the
substance from which the wire is made? Give your answer in scientific
notation to one decimal place.
We can recall that the resistivity
of a substance 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. We are given values for the
resistance, cross-sectional area, and the length. But before we substitute in these
values, we need to make sure that they are in appropriate units.
The resistance is given as 125
milliohms. So, we need to convert this value
into ohms by dividing by 1000. This will give us 0.125 ohms. The cross-sectional area is given
as 2.35 times 10 to the negative five meters squared, so the units here are
good. And the length of the wire is given
as 1.8 meters, so the units here are good. So we can now substitute these
values into this equation to calculate the resistivity of the substance. The resistivity is given by 0.125
ohms times 2.35 times 10 to the negative five meters squared divided by 1.8
meters. Completing this calculation gives
us 1.6 times 10 to the negative six ohmmeters to one decimal place.
So, the wire is made of a substance
with a resistivity of 1.6 times 10 to the negative six ohm meters.
