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 fifth meter squared. What is the resistivity of the substance from which the wire’s made?

Let’s begin by drawing a picture of our wire. In the diagram, we have labeled the length of the wire 𝐿 as 1.8 meters, the cross-sectional area of the wire 𝐴 as 2.35 times 10 to the negative fifth meter squared, the resistance of the wire 𝑅 as 125 milliohms, and we are looking for the resistivity of the wire 𝜌. In order to solve for resistivity, we need an equation that relates the resistance, resistivity, length, and cross-sectional area of our wire.

The equation that relates these four variables together is 𝑅, the resistance of the wire, equals 𝜌, the resistivity, times 𝐿, the length, divided by 𝐴, the cross-sectional area. We are solving for the resistivity. Therefore, we must rearrange our formula so that it solves for 𝜌. To do this, we multiply both sides of the equation by 𝐴 over 𝐿. This will cancel out both the 𝐴 and the 𝐿 on the right side of the equation, leaving us with the relationship 𝐴𝑅 over 𝐿 is equal to 𝜌. We can now substitute in our values for our variables.

For the cross-sectional area, we use 2.35 times 10 to the negative fifth meter squared. For the resistance, we use 125 milliohms, and 1.8 meters for the length. We need to be careful with our units. Right now our resistance is in milliohms, but it needs to be converted into ohms. Recall that the prefix milli- means 10 to the negative third. 125 milliohms is the same thing as 125 times 10 to the negative third ohms. After we multiply out our numerator and divide by our denominator, we get 1.63 times 10 to the negative six ohm meters for our resistivity.

The length in the problem was given to us to two significant figures. Therefore, we must report our resistivity to two significant figures. 1.63 times 10 to the negative sixth ohm meters rounds to 1.6 times 10 to the negative sixth ohm meters. The resistivity of the substance from which the wire is made is 1.6 times 10 to the negative sixth ohm meters.

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