Relation Between Resistance And Length

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

Resistance And Length

The resistance and length relation can be mathematically expressed as follows-

\(R= \frac{\rho L}{A}\)

Where,

  • 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/meter

Resistance And Length Relation

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

\(R\propto L\)

Which 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.

Resistance And Length Formula

The resistivity formula can be rearranged to get the relation between resistance and length. In short, It can be expressed along with symbol and units of resistance and length and symbol as-

Formula

Symbol

Unit

Resistance

\(R= \frac{\rho L}{A}\)

R

Ohm

Length

\(L=\frac{RA}{\rho }\)

L

Meter

Resistance and length of wire

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/meter.

Given,

Length of the wire L = 2 m

Cross-sectional area A = 1.7×10-5m2

Resistivity 𝜌 = 1.86×10-7Ohm/meter.

Substituting it in the resistance and length formula got by rearranging resistivity formula we get-

\(R= \frac{\rho L}{A}\) \(\Rightarrow R= \frac{1.86\times 10^{-7} \times2.0 }{1.7\times 10^{-5}}\) \(\Rightarrow R= 2.188\times 10^{-2}\)

Thus, the resistance of the wire is 2.188×10-2ohms.

Hope you understood the relation and conversion between resistance and length of any material.

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