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  4. E denotes electric field in a uniform conductor, I corresponding current through it, vd drift velocity of electrons and P denotes thermal power produced in the conductor. then which of the following graph is incorrect?

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

Current Electricity

Solution:

$E=\frac{I R}{L}=\frac{I . \rho}{A}=\frac{n e A v_{d} \rho}{A}$
$ \Rightarrow v_{d} \propto E$ (Straight line)
$P=I^{2} R=\left(\frac{E A}{\rho}\right)^{2} R \Rightarrow P \propto E^{2}$ (Symmetric parabola)
Also $P \propto I^{2}$ (parabola)
Hence, all graphs $a, b, d$ are correct and $c$ is incorrect.