Question

What is meant by electrical resistivity of a material? Derive its S.I. ​

Answer 1

Answer:

The electrical resistivity is the electrical resistance per unit length and per unit of cross-sectional area at a specified temperature. The SI unit of electrical resistivity is the ohm⋅metre (Ω⋅m). It is commonly represented bythe Greek letter ρ, rho. grendeldekt and 325 more users found this answer helpful.

Answer 2

Electrical resistivity:

Electrical resistivity is the property of an electrical material to resist the current.

This electrical resistivity depends on the nature of material and is

• Directly proportional to Resistance and Area
• Inversely proportional to length of the conductor.

So, we can say the formula of resistivity as:

$\pink{ \star} \: \boxed{ \red{ \bf{\rho = \dfrac{r \times a}{l} }}}$

where:

• ρ (Rho) is the electrical resistivity
• R is the resistance
• L is the length of the conductor
• A is the area of cross section.

S.I unit derivation:

We know that S.I unit of

★ Resistance is Ω (Ohm)

★ Area is m² (sq.metre)

★ Length is m (metre)

$\bf{\rho = \dfrac{r \times a}{l} }$

Substitute their S.I units.

$\dashrightarrow \: \tt{ \rho = \dfrac{ \Omega \times {m}^{2} }{m} }$

$\dashrightarrow \: \rm{ \rho = \dfrac{ \Omega \times m \times \cancel{m}}{ \cancel{m}} }$

∴ The unit of resistance is ‘Ω m’