In physics, resistance is the opposition offered to the flow of electricity. Length, on the other hand, is the physicalย 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.
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Resistivity Formula
The resistance and length relation can be mathematically expressed as follows-
\(\begin{array}{l}R= \frac{\rho L}{A}\end{array} \) |
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.
- ๐ 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.
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 symbols and units of resistance and length as-
| Formula | Symbol | Unit | |
Resistance |
\(\begin{array}{l}R= \frac{\rho L}{A}\end{array} \) |
R | Ohm |
Length |
\(\begin{array}{l}L=\frac{RA}{\rho }\end{array} \) |
L | Meter |
Practice Question
Calculate the value of resistance of a 2-meter-long wire with a cross-sectional area 1.7ร10-5m2 and resistivity 1.86ร10-7Ohm-metre.
Given,
Length of the wire L = 2 m
Cross-sectional area A = 1.7ร10-5m2
Resistivity ๐ = 1.86ร10-7Ohm/meter.
Substituting the values in the resistance and length formula got by rearranging the resistivity formula we get-
Thus, the resistance of the wire is 2.188ร10-2ohms.
Watch the video and solve important questions in the chapter Electricity Class 10
Hope you understood the relation and conversion between resistance and length of any material.
Physics Related Topics:
| Relation between Line Voltage and Phase Voltage |
| Relation Between Ev And Joule |
| Relation Between Watt And Volt |
| Relation Between Power And Resistance |
Frequently Asked Questions โ FAQs
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