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

NTA AbhyasNTA Abhyas 2020Current Electricity

Solution:

$E=\frac{V}{l}=\frac{I R}{l}=\frac{I \rho l}{Al}=\frac{n e A v_{d} \rho l}{Al}=nev_{d}\rho $
$v_{d} \, \propto E$ straight line
$P=I^{2}R=\left(\frac{E l}{R}\right)^{2}\times \, R=\frac{E^{2} l^{2}}{\rho l}\times A$
$\Rightarrow \, P \, \propto \, E^{2} \, \left(P a r a b o l a\right)$
$P \, \propto \, I^{2} \, \left(\right.Parabola)$