Question

The resistivity of the material of a wire is 2.77 × 10-8 Ωm. If the diameter of the wire is 1.20 mm and its length is 2.90 m, what is its resistance of the material in Ω?

Answer 1

Resistance of a wire is directly proportional to the length of the wire. But inversely proportional to the area of the wire.

R = (p . L) /A

Where p is resistivity of the wire, L is length, A is the area.

p = 2.77 x 10 ^{- 8} ohm . m

L = 2.90 m

Diameter = 1.20 mm

Radius is half of diameter = 0.6mm

1 m = 1000 mm

1 mm = 1/1000 m

0.6 mm = 0.6/1000 = 0.0006 m

Radius ' r ' = 0.0006 m

Area = π . r²

Area = π . (0.0006) ²

Area = 1.13 x 10 ^{- 6}   m2

So R = (p. L) /A

R =[ ( 2.77 x 10 ^{- 8} ) x (2.90 ) ]/ 1.13 x 10 ^{- 6}

R =0.07 ohm