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A conductor of length l is connected to a.d.c., source of potential V. if the length of the conductor is tripled by stretching it, keeping V constant, explain how to the following factors vary in the conductor? (i) Drift speed of electrons (ii) Resistance (iii) Resistivity. |
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Answer» Solution :When the wire is stretched to thrice its length, the area is reduced to one-third, `therefore ` Let `l_(1)=l,l_(2)=3,A_(1)=A,A_(2)=A//3` Now `R_(1)=rho(l_(1))/(A_(1)) and R_(2)=rho(l_(2))/(A_(2))` `(R_(2))/(R_(1))=((l_(2))/(l_(1)))xx((A_(1))/(A_(2)))=3xx3=9` i.e., RESISTANCE will become 9 times. Resistivity depends upon the NATURE of the material of the conductor and temperature. it does not depend upon the dimensions of the wire. since material of the wire and the temperature remain constant, hence resistivity will remain constant. Drift vel., `v_(d)=(eEtau)/(m)=(eVtau)/(ml)` Since, e,V,`tau` and m are constant, hence when length is TRIPLED, the drift velocity becomes `1/3`rd that of the ORIGINAL length. |
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