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(i) Derive expression for drift velocity of electrons in a conductor. Hence deduceohm's law . (ii) A wire whose cross-sectional area is increasinglinealy from itsone end to the other, is connectedacrossa batteryof V volts. Which of the followingquantities remains constantin the wire ? (a)drift speed , (b)current density (c ) electric current , (d) electricfield. Justify your answer. |
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Answer» Solution :(i) Consider an electron of mass m and chargee moving insidea conductorwith a driftvelocity`V_(d)` when an electricfield E is applied. Force on electron= eE. ma is the mechanical force the electron. `{:( :.,ma=eE,rArr,a=(eE)/m),("Now",v=u+at,,),("Here",u=0,,a=(eE)/(m)),(,t=tau(" relaxation time"),:.,u_(d)=(eE)/(m)tau):}` Ohm's law : `{:( :.,I="ne"Av_(d),:.,I="ne"(AEE)/(m)tau),( :.,I=("ne"^(2)AV)/(ml)tau,:.,R=V/IrArr (ml)/(A" ne"^(2)tau)),( :., V=(ml)/(" ne"^(2)Atau)I,:.,V prop I):}` Here Resistance `R =(ml)/(" ne"^(2)Atau)`. ltbgt(II) Currentdensity remainsconstant in the WIRE whose cross sectionalarea is increasing linearly from its one end to the other as , Current density `J = (I)/(A)`, It is currentper unit AREA,i.e, doesn't depend on area ofcross sectional . Drift speed `v_(d) = 1/(A"ne")` Electric field `= J//A`, is electricalconductivity. |
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