Question

A copper ,ribbon wire has breadth and length of 2mm and 0.5mm carries a current of 2A through it & has 10 m length . calculate resistance drift velocity and current density .​

Answer 1

Given:

l = 2mm

b = 0.5mm

i.e. A = l × b = 2 × 0.5 = 1 m$m^2$

Current I = 2A

l = 10 m

To find:

1) resistance drift velocity $V_d$ =?

2) current density J =?

Explanation:

1)

The resistance drift velocity is given by the formula

$\displaystyle V_d = \frac{I}{nqA}$

where

$V_d$ = resistance drift velocity

n = no of molecules

q = charge on the electron = 1.60×$10^{-19$ C

A = cross- sectional area

Put given values in above equation

$\displaystyle V_d = \frac{2}{1\times1.60\times10^{-19}\times(1\times10^{-3})^2}$

$\mathbf{V_d}$ = 1.25 × $\mathbf{10^{25}}$ m/s

2)

The current density is the electric current per unit cross-sectional area of a conductor.

$\displaystyle J = \frac{current}{area}$

   = $\displaystyle \frac{2}{1 \times 10^{-3}}$

J = 2000 A/$\mathbf{m^2}$