Video Transcript
A copper wire is 2.5 meters long
and has a cross-sectional area of 1.25 times 10 to the negative fifth meter
squared. Find the resistance of the
wire. Use 1.7 times 10 to the negative
eighth ohm meters for the resistivity of copper.
We’re asked to find a resistance,
and we’re given a length, a cross-sectional area, and a resistivity. Recall that we have a formula that
relates these four quantities. The resistance of an object, that
is, the ratio of an applied voltage to the current through the object, is equal to
the resistivity of the material making up the object, that is, its intrinsic
opposition to charge flow, times the length of the object divided by the object’s
cross-sectional area. Since we are given the length,
resistivity, and cross-sectional area, all we need to do to find the resistance is
plug in values.
So we have that the resistance is
1.7 times 10 to the negative eighth ohm meters times 2.5 meters divided by 1.25
times 10 to the negative fifth meter squared. 1.7 times 10 to the negative eighth
times 2.5 divided by 1.25 times 10 to the negative fifth is 3.4 times 10 to the
negative third. For the units, meters times meters
in the numerator divided by meter squared in the denominator is just one. And so we’re left with ohms, units
of resistance, which is what we’re looking for. To simplify our result a little
bit, recall that 10 to the negative third ohms is just one milliohm, so the
resistance of the copper wire is 3.4 milliohms. It’s important to recognize the
difference between mΩ, which is milliohms, a unit of resistance equal to one one
thousandth of an ohm, and Ω times m, which is ohm meters, a unit for
resistivity.
