Question

When a current flows in an aluminum wire of diameter 2.91 mm 2.91 mm , the drift speed of the conduction electrons is 0.000191 m/s 0.000191 m/s . How many electrons are flowing past a given point each second? The conduction electron density in aluminum is 6.00 × 10 28 m − 3 6.00×1028 m−3 .

Answer 1

Answer:

Number of electrons are flowing per second is 2.42 x 10¹⁹

Explanation:

The electric current flows through a wire is given by the relation :

$I=envA$   ....(1)

Here I is current, e is electronic charge, v is drift velocity of electrons and A is the Area of the wire.

But electric current is also define as rate of electrons passing through junction times their charge, i.e. ,

$I=Ne$      ....(2)

Here N is the rate of electrons passing through junction.

From equation (1) and (2).

$eN = envA$

$N=nvA$

But area of wire, $A=\pi \frac{d^{2} }{4}$

Here d is diameter of wire.

So, $N = nv\pi \frac{d^{2} }{4}$

Substitute 2.91 x 10⁻³ m for d, 0.000191 m/s for v and 6 x 10²⁸ m⁻³ for n in the above equation.

$N = 6\times10^{28}\times 0.000191\times\pi \frac{(2.91\times10^{-3} )^{2} }{4}$

N = 2.42 x 10¹⁹ s⁻¹