# Question Video: Resistance and Resistivity of Conductors Physics • 9th Grade

A copper wire is 2.5 m long and has a cross-sectional area of 1.25 × 10⁻⁵ m². Find the resistance of the wire. Use 1.7 × 10⁻⁸ Ω⋅m for the resistivity of copper.

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### 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.