Question

A metallic conductor has a resistivity of 35 × 10 −6 Ω⋅m. What is the resistance of a piece that is 20 m long and has a uniform cross-sectional area of 4.0 × 10 −6 m 2?

Answer 1

Answer:

Therefore the resistance of the conductor is 175Ω

Explanation:

Resistance:

• Resistance of a metallic conductor is directly proportional to its length(l).

• Resistance of a metallic conductor is inversely proportional to its cross section area(A).

The notation sign of resistance is R.

The unit of resistance is ohm (Ω).

Therefore,

$R \propto l$

and

$R \propto \frac{1}{A}$

$\therefore R\propto \frac{l}{A}$

$\Rightarrow R=\rho \frac{l}{A}$

ρ is the proportional constant.

It is also known as resistivity of that metal.

Given ρ=35×10⁻⁶Ω-m

l= 20 m

A= 4.0×10⁻⁶m²

$\therefore R=35\times 10^{-6}\times \frac{20}{4.0\times 10^{-6}}$

       =175Ω

Therefore the resistance of the conductor is 175Ω