Question

A 160 ft. long wire has a resistance of 16.2. What would the resistance of 8 ft. of wire be?

Answer 1

Resistance of 8 feet wire = 0.81 Ω

Explanation:

Equation representing the relation between the resistance and length of a cylindrical shaped wire is,

R = ρ.
`(l)/(A)`

Here R = Resistance of the cylindrical wire

ρ = Resistivity of the material

l = Length of the wire

A = Cross sectional area of the wire.

If length of the wire = 160 ft

Resistance = 16.2 Ω

By substituting these values in the formula,

16.2 = ρ.
`(160)/(A)`

ρ =
`(16.2* A)/(160)`

Similarly, if length of the same wire = 8 ft

From the given formula,

R = ρ.
`(8)/(A)`

R =
`(16.2* A)/(160)* (8)/(A)`

= 0.81 Ω

Therefore, resistance of 8 feet wire will be 0.82 Ω.