Current Electricity · Question 1

A metal wire of cross-sectional area 0.5 mm2 and length 100 m is connected across a battery of e.m.f. 2 V and internal resistance 1 . The density, atomic mass and electrical conductivity of the metal are 6.35 103 kg m-3, 63.5 gm/mole and 2 108 mho m-1, respectively. Assuming one conduction electron per atom of the metal, the drift velocity (in mm s-1) of the electrons in the wire is: [Take Avogadro’s number as 6 1023 and charge of the electron as 1.6 10-19 C.]

1. 0.052
2. 0.104
3. 0.208
4. 0.156

Answer

(3) 0.208

Solution

Key idea: R= L A, I= ER+r, vd= IneA.

R= 1002 108 0.5 10-6=1 , so I= 21+1=1 A.

n= NAM= 6.35 103 6 102363.5 10-3=6 1028 m-3.

vd= 16 1028 1.6 10-19 0.5 10-6= 14800 m s-1=2.08 10-4 m s-1=0.208 mm s-1.

Answer: (C)