Question

On what does te resistance depends upon ? Express it Mathematically and find the SI unit of rho

Answer 1

The resistance of aaterial depends upon the following points:
1)length is directly proportional
2) inversely proportional to area of cross section
3)the resistivity of the material used
4)with temperature its directly proportional.
(The fourth point is not used when determining the formula)
The formula will be,
R=¶×L/A
where L=length
A=area of cross section
¶=rho i.e. the resistivity of the material.
The formula of rho is ohm metre i.e Ωm
where,
Ω = ohm
m=metre
Derivation:
* R=¶×L/A
* R ×A/L=¶
* Ω×m2/m=¶
* Ω×m=¶
where,
Ω= the S.I. unit of resistance
m=the S.I. unit of length.