Question

A bar of certain material having rectangular cross section is one meter in length and has a cross section of 0.0001 square meters. The value of its longitudinal resistance is 100 ohms. The value of its resistivity would be *

Answer 1

The value of its resistivity would be 10⁶ ohm-m

Explanation:

We know that resistance

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

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

Given

Length of the bar l = 1 m

Cross sectional area of the bar A = 0.0001 m²

Resistance R = 100 ohms

Therefore, the resistivity of the bar

$\rho=100\times\frac{1}{10^{-4}}$

$\implies \rho=10^6$ ohm-m

Hope this answer is helpful.

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Answer 2

Given:

The longitudinal resistance of the material, R = 100 Ω

The area of cross-section, A = 0.0001 m²

The length of material, L = 1 m

To Find:

The value of resistivity, i.e., ρ of the material.

Calculation:

- The resistance of a conductor can be given by the formula:

R = ρ × L / A

⇒ ρ = R × A / L

⇒ ρ = 100 × 0.0001 / 1

⇒ ρ = 0.01 Ω m

- So, the resistivity of the material would be 0.01 Ω m.