Question

A 6.10 m length of 2.4 mm -diameter wire carries a 770 mA current when 22.0 mV is applied to its ends. The drift velocity is 2.0×10⁻⁵ m/s .

A. Determine the resistance R of the wire.

Express your answer to three significant figures and include the appropriate units.

B. Determine the resistivity ρ.

Express your answer to two significant figures and include the appropriate units.

C.Determine the current density j.

Express your answer to two significant figures and include the appropriate units.

D. Determine the electric field inside the wire.

Express your answer to two significant figures and include the appropriate units

E. Determine the number n of free electrons per unit volume.

Express your answer using two significant figures.

Answer 1

Given:

Length of conductor, l = 6.1 m

Diameter of cross section of wire = 2.4 mm

So, Area of cross section of wire, A = 3.14 * .0012 * .0012 square metres

A = 4.52 × 10^-6 sq.m

Current, I = 770 mA = 0.77 A

Potential difference, V = 22 mV

Drift velocity, v= 2× 10-5 m/s

(A) Ohm's law, V = I × R

Resistance, R = V/ I

R = 0.022 /0.77

R = 2.86 × 10^-2 ohms

(B) We have, R = ( * l )/A

Where, is resistivity

So, = (R *A)/ l

= 2.1 × 10^-8 ohm metre

The resistivity of wire is 2.1 × 10^-8 ohm metre.

(C) current density, j = I/A

j = 0.77/(4.52 × 10^-6 )

= 1.7 × 10⁵ Ampere per square metre

The current density is 1.7 × 10⁵ Amperes per sq.metre.

(D) We have , Electric field E = j ×

=  1.7 × 10⁵ ×2.1 × 10^-8

⁼ 3.6 × 10^-3 N/C

The electric field is 3.57 × 10^-3 N/C

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