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

A wire made of an unknown substance has a resistance of 125 mΩ. The wire has a length of 1.8 m and a cross-sectional area of 2.35 × 10⁻⁵ m. What is the resistivity of the substance from which the wire is made?

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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.

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