The following four wires are made of the same | vedclass

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(A) The resistance $R$ of a wire is given by the formula $R = \rho \frac{l}{A}$,where $\rho$ is the resistivity,$l$ is the length,and $A$ is the cross

Vedclass · Accepted Answer

Length = $50 \ cm$,diameter = $0.5 \ mm$

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(A) The resistance $R$ of a wire is given by the formula $R = \rho \frac{l}{A}$,where $\rho$ is the resistivity,$l$ is the length,and $A$ is the cross-sectional area.Since $A = \pi r^2 = \pi (d/2)^2 = \frac{\pi d^2}{4}$,we have $R \propto \frac{l}{d^2}$.For option $A$: $R_A \propto \frac{50}{(0.5)^2} = \frac{50}{0.25} = 200$.For option $B$: $R_B \propto \frac{100}{(1)^2} = 100$.For option $C$: $R_C \propto \frac{200}{(2)^2} = \frac{200}{4} = 50$.For option $D$: $R_D \propto \frac{300}{(3)^2} = \frac{300}{9} \approx 33.3$.Comparing these values,the ratio $\frac{l}{d^2}$ is maximum for option $A$. Therefore,the wire in option $A$ has the highest electrical resistance.

The following four wires are made of the same material and are at the same temperature. Which one of them has the highest electrical resistance?

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