Question

A Copper wire whose diameter is 0.16 cm carries a steady current of 20 A. What is the
current density of wire? Also calculate the drift velocity of the electrons in copper. n=8.1x10^28

Answer 1

Answer

Well follow my answer.

I hope this would be correct ans

Since the two wires are joined in series the current through each wire is the same i.e. I=10A

(a) For copper wire A=πD2/4,

current density J=I/A=I/(πD2/4)

(b) For aluminum wire , A'=πD2/4

=π(0.25×10−2)2/4

=2.01×10−6m2,n=1029m−3

Drift velocity, υd=I/nA'e

Answer 2

Given info : A copper wire whose diameter is 0.16cm carries a steady current of 20A and electrons density is 8.1 × 10²⁸ /m³.

To find : the current density of the wire and the drift velocity of the electrons are..

solution : current density is the value of current flowing through a unit area of a chosen cross section.

i.e., current density, J = i/A

where, i is the current flowing through a wire and A is the cross sectional area of that wire.

here, current, i = 20A

diameter of wire, d = 0.16 cm = 16 × 10⁻⁴ m

∴ cross sectional area of the wire, A = πd²/4 = 3.14 × (16 × 10⁻⁴ m)²/4

   = 3.14 × 4 × 10⁻⁸ m² = 1.256 × 10⁻⁷ m²

∴ the current density of the wire, J = 20/(1.256 × 10⁻⁷) A/m² ≈ 16 × 10⁷ A/m²

drift velocity,   $v_d=\frac{i}{neA}$

e = charge of electron = 1.6 × 10⁻¹⁹ C

∴ drift velocity = $\frac{20A}{8.1\times10^{28}/m^3\times1.6\times10^{-19}C\times1.256\times10^{-7}m^2}$

                      = 0.0123 m/s

therefore the drift velocity of the electrons is 0.0123 m/s