A uniform metal wire of length 20\,\text{m} and total mass 0.034\,\text{kg} is manufacture… — JAMB UTME

A uniform metal wire of length $20\,\text{m}$ and total mass $0.034\,\text{kg}$ is manufactured from a material of density $8.5 \times 10^3\,\text{kg/m}^3$ and electrical resistivity $1.7 \times 10^{-8}\,\Omega\cdot\text{m}$ . What is the electrical resistance of the wire in ohms?

Answer: 1.7 Ω

Answer

The electrical resistance of the wire is

1.7\,\Omega

Combining the density relation

V = \frac{m}{d}

with the geometric expression

V = A \cdot L

gives

A = \frac{m}{d L}

. Substituting this into Pouillet's law

R = \frac{\rho L}{A}

yields

R = \frac{\rho d L^2}{m}

. Evaluating with the given values:

R = \frac{(1.7 \times 10^{-8})(8.5 \times 10^3)(20)^2}{0.034} = 1.7\,\Omega

Step-by-Step Solution

Calculate the volume of the wire using mass and density

V = 4.0 \times 10^{-6}\,\text{m}^3

Volume is related to mass and density by

V = \frac{m}{d}

Calculate the cross-sectional area of the wire

A = 2.0 \times 10^{-7}\,\text{m}^2

For a cylindrical wire of uniform cross-section,

V = A \cdot L

, so

A = \frac{V}{L}

Apply resistivity formula to find electrical resistance

R = 1.7\,\Omega

Resistance is given by

R = \frac{\rho L}{A}

Key Concept

Relationship between Resistance, Mass, Density, and Resistivity

Estimated Time:2m 0s

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Topics

More questions from this topic