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Theory:

1. Nature of a conductor:
The resistance of a conductor varies for different types of materials, depending on their nature.
In electrical experiment, it can be easily proved that the conductor's resistance (\(R\)) is directly proportional to its length (\(L\)) and inversely proportional to its area of cross-section (\(A\)).
RαLRα1A
 
2. Length of a conductor:
The conductor's resistance (\(R\)) is directly proportional to its length (\(L\)).
 
2_resistors_in_series.png
Circuit with resistors
 
Consider the length of two conductors to be \(L_{1}\) and \(L_{2}\), having a resistance of \(R_{1}\) and \(R_{2}\), respectively. Assume that the conductors are made of the same material. Then,
 
R1αL1R2αL2R1R2=L1L2
 
3. Area of cross-section of the conductor:
The conductor's resistance (\(R\)) is inversely proportional to its area of cross-section (\(A\)).
 
Let the cross-sectional area of two conductors to be \(A_{1}\) and \(A_{2}\), having a resistance of \(R_{1}\) and \(R_{2}\), respectively.
 
R1α1A1R2α1A2R1R2αA2A1
 
Since the area of cross-section of a conductor is A=πr2, where \(r\) is the radius of the conductor.
 
Here, \(r_{1}\) and \(r_{2}\) be the radii of two conductors. On substituting this value in the above equation, we get
 
R1R2=A2A1R1R2=πr22πr12=r2r12
 
On combining both the equations of the second and third factors, we get
 
RαLAR=(constant)LA
 
R=ρLA ---- (eq. 1)
 
The constant of proportionality is given as \(\rho\) in the above equation. It is known as an electrical resistivity or specific resistance of the material of the conductor.
 
The (eq. 1) can be written as,
 
ρ=RAL
 
If \(L\) \(=\) \(1\ m\), \(A\) \(=\) \(1\ m^2\) then, the above equation becomes \(\rho\) \(=\) \(R\).
The electrical resistivity of a material is defined as the resistance of a conductor of unit length and unit area of cross-section.
Unit:
The SI unit of resistivity is ohm metre or Ωm.
 
Unitofρ=R×AL=ohm×metre2metre=ohmmetre(Ωm)
 
A conductor's electrical resistivity is a measurement of its resistance to the passage of an electric current. The electrical resistivity of a material is always constant and independent of its size and shape.
 
Important!
Nichrome has the highest electrical resistivity, equal to 1.5×106Ωm. Hence, this conducting material is used in making heating elements.
springs-extension-metal-spiral.jpg
Nichrome coil
Reference:
https://upload.wikimedia.org/wikipedia/commons/5/5a/2_resistors_in_series.png