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(C) The resistance $R$ of a wire is given by the formula $R = \rho \frac{l}{A} = \rho \frac{l}{\pi r^2}$,where $\rho$ is the resistivity,$l$ is the le

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Radius $1 \, mm$ and length $80 \, m$.

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(C) The resistance $R$ of a wire is given by the formula $R = \rho \frac{l}{A} = \rho \frac{l}{\pi r^2}$,where $\rho$ is the resistivity,$l$ is the length,and $r$ is the radius.Since all wires are made of the same material,$\rho$ is constant.For option $A$: $R_A \propto \frac{40}{1^2} = 40$.For option $B$: $R_B \propto \frac{40}{2^2} = 10$.For option $C$: $R_C \propto \frac{80}{1^2} = 80$.For option $D$: $R_D \propto \frac{80}{2^2} = 20$.Comparing the values,$R_C$ is the highest. Therefore,the wire with radius $1 \, mm$ and length $80 \, m$ has the highest resistance.

Which of the following wires made of the same material will have the highest resistance?

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