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(C) The electric field $E$ in a conductor is given by $E = \frac{V}{L} = \frac{IR}{L} = \frac{I \rho}{A}$.Since $I = neA{v_d}$,we have $E = \frac{(neA

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(C) The electric field $E$ in a conductor is given by $E = \frac{V}{L} = \frac{IR}{L} = \frac{I \rho}{A}$.Since $I = neA{v_d}$,we have $E = \frac{(neA{v_d}) \rho}{A} = ne\rho{v_d}$. Thus,${v_d} \propto E$,which is a straight line passing through the origin.Thermal power $P$ is given by $P = I^2R$. Substituting $I = neA{v_d}$,we get $P = (neA{v_d})^2 R = (neA)^2 R {v_d}^2$. Thus,$P \propto {v_d}^2$,which represents a parabola.Also,$P = I^2R$,so $P \propto I^2$,which is a parabola.Finally,$P = \frac{V^2}{R} = \frac{(EL)^2}{R} = \frac{L^2}{R} E^2$. Thus,$P \propto E^2$,which is a parabola.Comparing these with the given options,the graph of $P$ versus ${v_d}$ should be a parabola,but option $C$ shows a straight line. Therefore,graph $C$ is incorrect.

If $E$ denotes the electric field in a uniform conductor,$I$ the corresponding current through it,${v_d}$ the drift velocity of electrons,and $P$ the thermal power produced in the conductor,then which of the following graphs is incorrect?

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