Class 12 Physics
CBSE and UP Board
Current Electricity
Exercise 3
Chapter-3 Exercise 3.13
The number density of free electrons in a copper conductor estimated in Example 3.1 is 8.5 × 10²⁸ m⁻³. How long does an electron take to drift from one end of a wire 3.0 m long to its other end? The area of cross-section of the wire is 2.0 × 10⁻⁶ m² and it is carrying a current of 3.0 A.
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Number density of free electrons in a copper conductor, n = 8.5 x 1028 m–3 Length of the copper wire, I = 3.0 m
Area of cross-section of the wire, A = 2.0 x 10-6 m2
Current carried by the wire, I = 3.0 A, which is given by the relation, I = nAeVd Where, e = Electric charge = 1.6 x 10-19 C
Vd= Drift Velocity = Length of the wire (l) /Time taken to cover l (t)
I = nAel/t => t = nAel/t
t = 3x 8.5 x 1028 x 2 x 10-6 x 1.6 x 10-19 )/3.0
= 2.7 x 10⁴ s
Therefore, the time taken by an electron to drift from one end of the wire to the other is 2.7 x 104 s.