Question

2. A 5.80 m length of 2.0 mm diameter wire carries a 750 mA current when 22.0 mV is applied to its ends. I
the drift speed is 1.7 x 10-5 m/s, determine
(a) The resistance R of the wire
(b) The resistivity p, and
(c) The number n of free electrons per unit volume.​

Answer 1

Given :

length of wire = 5.8 m

diameter of wire = 0.002 m

current , I = 750 mA

volatge , V = 22 mV

drift speed , v = 1.7 x 10^(-5) m/s  

To find :

(a) The resistance R of the wire

(b) The resistivity p

(c) The number n of free electrons per unit volume.​

Solution :

(a).  V = I * R

    22 mV = 750 mA * R

    R = 22 / 750 ohm

       = 0.294 ohm

(b). R = ( p * l ) / ( area of cross section of wire )

    0.294 = p * 5.8 / ( 3.14 * 0.001 * 0.001 )

     p = 0.294 * 3.14 * 10^(-6) / 5.8

        = 1.59 x 10^ (-7) ohm m

(c) drift velocity , v = I / ( n * q * A )

where , I is current ,

n is number of free electrons per unit volume​ ,

q is charge of electron ,

A is area of cross section of wire .

now ,

n = I / ( v * q * A )

  = 8.78 x 10 ^ 28

(a) The resistance R of the wire  is 0.294 ohm

(b) The resistivity p is 1.59 x 10^ (-7) ohm m

(c) The number n of free electrons per unit volume is 8.78 x 10 ^ 28