Question

How long does it take electrons to get from the car battery to the starting motor? Assume the current is 149 A and the electrons travel through copper wire with cross sectional area 36.3 mm2 and length 82 cm . The mass density of copper is 8960 kg/m3 and the molar mass is 63.5 g/mol . Avogadro’s number is 6.022 × 1023 . Assume that each copper atom contributes one conduction electron. Answer in units of min.

Answer 1

Current I through wire of cross section A is given by , I = n e A vd ............(1)

where n is number density of electron , e is charge on electron , A is area of cross section and vd is drift velocity.

Number density in copper wire is calculated as follows.

Density of copper = 8690 kg/m3

number of atoms in 1 kilo mole copper , i.e. 63.5 kg has 6.022 1026

Hence number of density of atoms in copper wire = ( 6.022 1026 / 63.5 ) 8690

number of density of atoms in copper wire = 8.24 1028

If each copper atom contributes 1 electron , then number density n of electron is given by ,

n = 8.24 1028

Drift velocity vd = I / ( n e A ) = 149 / ( 8.24 1028 1.602 10-19 36.3 10-6 )

Drift velocity vd = 0.311 10-3 m/s

Time taken to travel 82 cm length of wire = 82 10-2 / 0.311 10-3 2637 s

Time taken to travel 82 cm length of wire = 44 min