JEE Main2015PhysicsCurrent ElectricityActual
When 5 V potential difference is applied across a wire of length 0 . 1 m , the drift speed of electrons is 2.5 × 10 - 4 m s - 1 . If the electron density in the wire is 8 × 10 28 m - 3 , the resistivity of the material is close to:
Options
- A1 .56 × 10 - 5   Ω   m
- B1 .6 × 10 - 8   Ω   m
- C1 .6 × 10 - 7   Ω   m
- D1 .6 × 10 - 6   Ω   m
Correct answer
A. 1 .56 × 10 - 5   Ω   m
Step-by-step solution
Potential difference =   5   V , length = 0.1 m = l and the electron speed = drift velocity v d = 2.5 × 1 0 - 4   m s - 1 , electron density n = 8 × 1 0 2 8 m - 3 and the charge on each electron(e) = 1.6 × 1 0 - 1 9   C . We know i = nAe v d     . . . ( i ) . And V = i R                 . . . ( ii ) Resistance R is also equal to, ρ l A ⇒ R = ρ l A ρ = AR l ρ = Resistivity = A l × V i [from (