Question

Calculate the resistance of 2 m long copper wire of radius 1 mm. Resistivity of copper is 1.72 x 10-8 ohm-m.​

Answer 1

R = 1.095 × 10^-2 ohm is the required answer.

GIVEN:

• Length of copper wire, l = 2 m
• Radius , r = 1 mm = 10^-3 m
• Resistivity, ρ = 1.72 × 10^-8 ohm m

TO FIND:

Resistance of copper wire, R

FORMULAE:

• Area , A = π r²
• Resistance, R = ( ρl ) /A

SOLUTION:

STEP 1: TO FIND AREA:

A = π r²

$= 3.14 \times { ({10}^{ - 3} )}^{2} \\ \\ area= 3.14 \times {10}^{ - 6} {m}^{2}$

Area , A = 3.14 × 10^-6 m²

STEP 2: TO FIND RESISTANCE:

R = ( ρl ) /A

$= \frac{1.72 \times {10}^{ - 8} \times 2}{3.14 \times {10}^{ - 6} } \\ \\ = \frac{3.44}{3.14} \times {10}^{ - 8} \times {10}^{6} \\ \\ = 1.095 \times {10}^{ (- 8 + 6)} \\ \\ R= 1.095 \times {10}^{ - 2} ohm$

ANSWER:

Resistance of coper wire , R = 1.095 × 10^-2 ohm

RESISTANCE:

• It is the measure of resistance offered to the flow of current through the conductor.

• It depends on physical parameters like length and radius of conductor.

• Its unit is ohm.

• Resistance increases with increase in temperature and decreases with decrease in temperature.

RESISTIVITY:

• It is defined as the resistance offered to flow of current through conductor having unit length and unit area of cross section.

• It is constant for a given type of conductor.

• It does not change with change in values of physical parameters of conductor.

• Resistivity is directly proportional to temperature.

• Its unit is ohm m