Relation Between Current and Drift Velocity
Relation Between Current and Drift Velocity :- Let a battery of e.m.f. V is applied across a conductor of length L. An electric field E (= V/L) is set up inside the conductor and the electrons drift towards the positive terminal of the battery with drift velocity vd.
L = length of the conductor
A = area of cross-section of the conductor
n = number of free electrons per unit volume of the conductor
V = potential difference applied across the conductor
vd = drift velocity of the electrons
∴ Total number of free electrons in the conductor = nAL
Total free charge in the conductor (Q) = nALe
Time taken by an electron to cross the conductor, t = L/vd
Current flowing in the conductor, I = Q/t = nALe/(L/vd)
I = neAvd
This is the required relation between current and drift velocity.
Find free electrons per unit volume in a metallic wire of density 104 kg/m3, atomic mass number 100 and number of free electron per atom is one.
Number of free electrons per unit volume (n) = total free charge particles/total volume
∴ Number of free electron per unit volume (n) = total number of atoms per unit volume (as given in question that there is one free electron per atom)
Total number of atoms(N), is given by
∴ Number of free electron per unit volume (n) = N/V
n = 6.023 × 1028
A current of 1.34 A exists in a copper wire of cross–section 1.0 mm2. Assuming each copper atom contributes one free electron, calculate the drift speed of the free electrons in the wire. The density of copper is 8990 kg/m3 and atomic mass = 63.50.
As I = neAvd
Here n = number of free electrons per unit volume
⇒ n = number of copper atoms per unit volume of the wire (as given in the question)
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