Question

Resistance of a wire of length 5m and radius of cross section 0.15 mm at room temperature is 28 Ω. Calculate the resistivity of the material of the wire and express in S.I unit.

Answer 1

Step-by-step explanation:

given:-

R=28 Ω

l = 5m

Cross Section = 0.15 mm = 0.15×10^-3m

Area = 3.14 × 0.00015² = 7.07×10^-7 m²

resistivity = p = ?

R = p l/A

p = R×A/l

p = 28 × 7.07×10^-7 / 5

p = 3.95×10^-7 Ωm or 4 × 10^-7 (nearly)

Answer 2

The required answer is 3956.4 × 10^-10 ohm m

GIVEN:

•Length, l = 5 m

•Radius of cross section, r = 0.15 mm

•Resistance of wire , R = 28 ohm

TO FIND:

Resistivity of the material , ρ

FORMULA:

Resistance , $R\: =\: \frac{\rho\:l}{A}$

KEYS:

• R is the resistance of wire

• l is the length of wire

• r is radius of wire

• A is the area of cross section of wire

• ρ is the resistivity

SOLUTION:

STEP 1: TO CONVERT THE RADIUS IN STANDARD UNIT

$1\: mm\: =\:10^-3\: m\\</p><p>0.15\: mm\: =\: 0.15\times10^-3\: m\\</p><p>So\: radius\: ,\: r \:=\: 0.15\times10^-3\:m$

STEP 2: TO FIND AREA

$Area\:=\: \pi \times r^2\\\\</p><p>\pi\: =\: 3.14\\\\</p><p>Area \: =\: 3.14\times(0.15\times10^-3)^2\\ \\</p><p>A\: =\: 3.14\times0.15\times0.15\times10^-6\\ \\</p><p>A\: =\: 0.07065\times10^-6\\ \\</p><p>A\: =\: 706.5\times10^-4\times10^-6\\ \\</p><p>A\: =\: 706.5\times10^-10\:m^2</p><p>$

STEP 3: TO FIND RESISTIVITY

$R\:=\:\frac{\rho\: l}{A}\\\\</p><p>\rho\:=\:\frac{RA}{l}\\\\</p><p>=\:\frac{28\times706.5\times10^-10}{5}\\\\</p><p>=\:28\times141.3\times\times10^-10\\\\</p><p>\rho\:=\:3956.4\times10^-10\: \Omega\:m</p><p>$

ANSWER:

THE RESISTIVITY OF THE MATERIAL IS 3956.4 × 10^-10 Ohm m.

FACTS RELATED TO QUESTION:

RESISTIVITY:

• Resistivity is defined as the resistance offered to the flow of current through a material of length 1 m and having uniform area of cross section of 1 m²

• It's value is constant for a given material.

• Its value doesn't change with change in physical parameters of conductor like length, area of cross section and radius.

• It's SI unit is ohm m.

• Resistivity of conductor increases with increase in temperature.