Suppose the drift velocity v_d in a material | vedclass

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(C) The current $I$ is related to the drift velocity $v_d$ by the formula $I = n e A v_d$,where $n$ is the charge carrier density,$e$ is the charge,an

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(C) The current $I$ is related to the drift velocity $v_d$ by the formula $I = n e A v_d$,where $n$ is the charge carrier density,$e$ is the charge,and $A$ is the cross-sectional area.Given that $v_d \propto \sqrt{E}$,we can substitute this into the current equation:$I \propto v_d \propto \sqrt{E}$Since the electric field $E$ is related to the potential difference $V$ across a wire of length $L$ by $E = V/L$,we have $E \propto V$.Substituting this into the proportionality for current:$I \propto \sqrt{V}$Squaring both sides,we get:$I^2 \propto V$This represents a parabolic relationship where $V$ is proportional to the square of $I$ $(V = k I^2)$. This corresponds to a curve that is concave up,starting from the origin. Among the given options,the graph that shows $V$ increasing more rapidly than $I$ (a parabolic curve opening upwards) is the correct one.

Suppose the drift velocity $v_d$ in a material varies with the applied electric field $E$ as $v_d \propto \sqrt{E}$. Then the $V-I$ graph for a wire made of such a material is best given by:

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