Question Video: Resistance and Resistivity of Conductors | Nagwa Question Video: Resistance and Resistivity of Conductors | Nagwa

Question Video: Resistance and Resistivity of Conductors Physics • Third Year of Secondary School

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A copper wire with a resistance of 12.8 mΩ has a cross-sectional area of 1.15 × 10⁻⁵ m². Find the length of the wire. Use 1.7 × 10⁻⁸ Ω⋅m for the resistivity of copper.

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Video Transcript

A copper wire with a resistance of 12.8 milliohms has a cross-sectional area of 1.15 times 10 to the negative five meters squared. Find the length of the wire. Use 1.7 times 10 to the negative eight ohm meters for the resistivity of copper. Give your answer to one decimal place.

We can recall that the resistivity of a material 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. So, if we rearrange this equation, we can calculate the length of the wire. If we multiply both sides of the equation by the length 𝐿, then this cancels on the right. If we then divide both sides by the resistivity ρ, then this cancels on the left. And we find that 𝐿 is equal to 𝑅 times 𝐴 divided by ρ.

We are given values for the resistance, cross-sectional area, and resistivity. But before we substitute in these values, we need to make sure that they are in appropriate units. The resistance is given as 12.8 milliohms. So, we need to convert this value into ohms by dividing by 1000. This will give us 0.0128 ohms. The cross-sectional area is given as 1.15 times 10 to the negative five meters squared, so the units here are good. And the resistivity is given as 1.7 times 10 to the negative eight ohm meters, so the units here are good. So, we can now substitute these values into this equation to calculate the length of the wire.

The length of the wire is given by 0.0128 ohms times 1.15 times 10 to the negative five meters squared divided by 1.7 times 10 to the negative eight ohm meters. Completing this calculation gives us 8.7 meters to one decimal place. So, the length of the wire is 8.7 meters.

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