Question

A 1.5-cm square rod, 4.0 m long, measures 0.040 ohms. What is its resistivity?

Answer 1

Answer:

2.25 × 10⁻⁶ Ω m

Explanation:

Given :

Length of rod = 4 m

Area = 1.5 × 1.5 cm² = 2.25 × 10⁻⁴ m²

Resistance = 0.040 Ω = 4 × 10⁻² Ω

We are asked to find Resistivity :

We know :

R = ρ L / A

= > ρ = R × A  / L

Putting values here we get :

= > ρ = 4 × 10⁻² × 2.25 × 10⁻⁴ / 4 Ω m

= > ρ =  10⁻² × 2.25 × 10⁻⁴ Ω m

= > ρ =  2.25 × 10⁻⁶ Ω m

Therefore , Resistivity of rod is 2.25 × 10⁻⁶ Ω m .

Answer 2

Answer :-

2.25 * 10^( - 6 ) Ω - m.

Solution :-

Given :

Cross section area ( A ) = 1.5 cm * 1.5 cm = 2.25 cm² = 2.25 * 1/10^4 = 2.25 * 10^( - 4 ) m²

[ Because 1 cm² = 1/10^4 m² ]

Length of the rod ( l ) = 4 m

Resistivity ( ρ ) = ?

Resistance ( R ) = 0.040 Ω

Also, R = ρl/A

$\implies 0.040 = \rho \times \dfrac{4}{2.25 \times {10}^{ - 4} }$

$\implies \dfrac{4}{100} = \rho \times \dfrac{4}{2.25 \times {10}^{ - 4} }$

$\implies 4 \times {10}^{ - 2} = \rho \times \dfrac{4}{2.25 \times {10}^{ - 4} }$

$\implies {10}^{ - 2} \times 2.25 \times {10}^{ - 4} = \rho$

$\implies 2.25 \times {10}^{ - 6} = \rho$

$\implies \rho = 2.25 \times {10}^{ - 6}$

Therefore the resistivity of the rod is 2.25 * 10^( - 6 ) Ω - m