Relation between Resistance and Length

In physics, resistance is the opposition offered to the flow of electricity. Length, on the other hand, is the physical dimensional measurement of extension between two points. The relation between length and resistivity is given by the resistivity formula. Resistance is directly proportional to the length. This means that any change in the length of the material will change its value of resistance.

Resistivity Formula

• R is the resistance measured using ohms.
• L is the length of the material measured using the meter.
• A is the cross-sectional area measured in m².
• 𝜌 is the resistivity of the material measured using ohm-metre

Resistance And Length Relation

For a given material,the resistance and length formula clearly speaks that the resistance is directly proportional to its length.

This implies that-

• When the length of the material is increased, its value of resistance also increases.
• When the length of the material decreases, its value of resistance will also decrease.

Practice Question

Calculate the value of resistance of a 2-meter-long wire with a cross-sectional area 1.7×10^-5m² and resistivity 1.86×10^-7Ohm-metre.

Given,

Length of the wire L = 2 m

Cross-sectional area A = 1.7×10^-5m²

Resistivity 𝜌 = 1.86×10^-7Ohm/meter.