The graph showing the variation of resistance | vedclass

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

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(C) The resistance $(R)$ of a wire is given by the formula: $R = \frac{\rho \ell}{A}$,where $\rho$ is resistivity,$\ell$ is length,and $A$ is the cross-sectional area.Since the wire is cylindrical,the cross-sectional area $A = \pi r^2 = \pi (D/2)^2 = \frac{\pi D^2}{4}$.Substituting this into the resistance formula,we get: $R = \frac{\rho \ell}{\pi D^2 / 4} = \frac{4 \rho \ell}{\pi D^2}$.Since $\rho$,$\ell$,and $\pi$ are constants,we have $R \propto \frac{1}{D^2}$.This relationship represents an inverse square law,which corresponds to a curve that decreases as $D$ increases. Among the given options,Graph $C$ represents this behavior.

The graph showing the variation of resistance $(R)$ of a metal wire as a function of its diameter $(D)$,while keeping other parameters like length and temperature constant,is:

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