Question

calculate the resistivity of wire 1.0mm long and 0.4mm is the diameter having te resistance of 2ohm​

Answer 1

Answer:

2.513×10^(-4) ohm m

Explanation:

Use the formula -

R = ρl/A

where, R = resistance (in ohm)

ρ = resitivity (ohm metre)

l = length of the wire (in metres)

A = Area of cross section (in metres squared)

Answer 2

Answer:

Resistivity of the wire = 2.51 × 10⁻⁴ Ω m

Explanation:

Given:

• Length of wire = 1 mm = 1 × 10⁻³ m
• Diameter = 0.4 mm = 4 × 10⁻⁴ m
• Resistance = 2 Ω

To find:

• Resistivity of the wire

Solution:

First we have to find the area of the cross section of the wire

The radius of the wire = 4 × 10⁻⁴ m/2 = 2 × 10⁻⁴ m

Now area of cross section = π r²

Substituting the data,

Area of cross section of wire = 3.14 × (2 × 10⁻⁴)²

Area of cross section of wire = 3.14 × 4 × 10⁻⁸

Area of cross section = 1.256 × 10⁻⁷ m²

Now the equation for finding resistivity is given by,

R = ρ l/A

where R is the resistance

           ρ = Resistivity

           l = length of the conductor

           A = area of cross section

Substituting the data,

2 = ρ × 1 × 10⁻³/1.256 × 10⁻⁷

2 = ρ × 7961.8

ρ = 2/7961.8

ρ = 2.51 × 10⁻⁴ Ω m

Hence the resistivity of the conductor is 2.51 × 10⁻⁴ Ω m.

Notes:

The resistance of a conductor is directly proportional to the length of the conductor.

The resistance of a conductor is inversely proportional to the area of cross section of the conductor.

R = ρ l/A