Question

Assume that each atom of copper contributes one free electron. If the current flowing through a copper wire of 1 mm diameter is 1.1 A, the drift velocity of electrons will be (density  of Cu = 9 gm/cm³, At. wt. of Cu = 63) 

1. 0.3 mm/s
2. 0.5 mm/s
3. 0.1 mm/s
4. 0.2 mm/s

Answer 1

Correct Answer - Option 3 : 0.1 mm/s

CONCEPT:

• Drift velocity is the average velocity attained by a charged particle in a conductor under an applied electric field and is given by

\(⇒ V_{d} = \frac{eEτ}{m}\)

Where e = charge E = Electric field, τ = Relaxation time, m = mass

• The relationship between current and drift velocity is given by

⇒ I = neAV_d

Where I = Current, n = charge density, A = Area, e = charge 

CALCULATION:

Given - ρ = 9 gm/cm³ = 9 × 10³ Kg/m³, I = 1.1 A, d = 1 mm ,  radius, r = 0.5 mm = 0.5 × 10^-3 m , M = 63 = 63 × 10^-3kg, and N_A = 6.023 × 10²³

• The charge density of the copper is given by

\(⇒ n = \frac{N_{A} \rho}{M}\)

Substituting the given values in the above equation

\(⇒ n = \frac{6 .023\times 10^{23}\times 9\times 10^{3}}{63\times 10^{-3}} = 8.6\times 10^{28} m^{-3} \)

• The amount of current produced is given by

⇒ I = neAVd

\(⇒ V_{d} = \frac{I}{neA} = \frac{1.1}{8.6\times 10^{28}\times 1.69\times 10^{-19}\times \pi\times (0.5\times 10^{-3})^{2}} = 0.1\times 10^{-3} m/s\)

\(⇒ V_{d} = 0.1 mm/s\)

• Hence, option 3 is the answer