Answer:
a) Current in wire 1 = 0.132 A
Current in wire 2 = 0.101 A
b) Resistance of wire 1 = R₁ = 0.000376 Ω = (3.76 × 10⁻⁴) Ω = 0.376 mΩ
Resistance of wire 2 = R₂ = 0.000495 Ω = (4.95 × 10⁻⁴) Ω = 0.495 mΩ
Explanation:
Current density, J = (current) × (cross sectional area)
Current density for both wires = J = 2950 A/m²
For wire 1,
Cross sectional Area = πr² = π(0.00378²)
A₁ = 0.00004491 m²
For wire 2,
With the assumption that the strands are well banded together with no spaces in btw.
Cross sectional Area = 19 × πr² = π(0.000756)²
A₂ = 0.00003413 m²
Current in wire 1 = I₁ = J × A₁ = 2950 × 0.00004491 = 0.132 A
Current in wire 2 = I₂ = J × A₂ = 2950 × 0.00003413 = 0.101 A
b) Resistance = ρL/A
ρ = resistivity for both wires = (1.69 x 10⁻⁸) Ω.m
L = length of wire = 1.00 m for each of the two wires
A₁ = 0.00004491 m²
A₂ = 0.00003413 m²
R₁ = ρL/A₁ = (1.69 x 10⁻⁸ × 1)/0.00004491
R₁ = 0.000376 Ω = (3.76 × 10⁻⁴) Ω = 0.376 mΩ
R₂ = ρL/A₂ = (1.69 x 10⁻⁸ × 1)/0.00003413
R₂ = 0.000495 Ω = (4.95 × 10⁻⁴) Ω = 0.495 mΩ
Hope this helps!!
