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Question
A conductor of length ‘l’ is connected to a dc source of potential ‘V’. If the length of the conductor is tripled by gradually stretching it, keeping ‘V’ constant, how will (i) drift speed of electrons and (ii) resistance of the conductor be affected? Justify your answer.
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Solution
V = constant
l’ = 3l
(i) Drift speed of electrons `= V/("nel" rho)`
Where n is number of electrons
e is charge on electron
l is the length of the conductor
and ρ is the resistivity of conductor.
So, when length is tripled, drift velocity gets one-third.
(ii) Resistance of the conductor is given as
`R =rho l/A`
When length is tripled area of cross-section is reduced to `A/3`
Hence, `R = rho (l')/(A') = rho(3l)/(A/3) = 9rhol/A =9R`
Thus, new resistance will be 9 times the original.
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