Question

The resistance of a wire depends upon the material's resistivity and the length and cross‑sectional area of the wire. What will happen to the resistance of a wire if its length is multiplied by 4?

Answer 1

Answer:

R' = 4R

The resistance will become 4 times the initial value.

Explanation:

The resistance of a wire at room temperature, is given by the following formula:

R = ρL/A   ----------- equation 1

where,

R = Resistance of wire

ρ = resistivity of the material

L = Length of wire

A = Cross-sectional area of wire

Now, if the length (L) is multiplied by 4, then resistance will become:

R' = ρ(4L)/A

R' = 4 (ρL/A)

using equation 1:

R' = 4R

The resistance will become 4 times the initial value.