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

The resistance of a wire will quadruple if its length is multiplied by 4.

Step-by-step explanation:

The resistance of a wire is directly proportional to its length and inversely proportional to its cross-sectional area. According to Ohm's Law, resistance (R) is given by the equation R = ρ * (L/A), where ρ is the resistivity of the material, L is the length of the wire, and A is the cross-sectional area of the wire. If the length of the wire is multiplied by 4, the resistance will also quadruple. This is because increasing the length of the wire increases the number of collisions charges make with its atoms, resulting in a higher resistance.

Answer 2

R' = 4R

The resistance will become 4 times the initial value.

Step-by-step 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.