1.What equal length of iron wire and a constantan wire each of 1mm diameter must br joined in parallel to give an eqivalent resistance of 2 Ohm? If the resistivities of iron and constantan are 10 and 49 micro ohm-cm respectively.
Answers
1.What equal length of iron wire and a constantan wire each of 1mm diameter must br joined in parallel to give an eqivalent resistance of 2 Ohm? If the resistivities of iron and constantan are 10 and 49 micro ohm-cm respectively.
R = ρ L /A
L = ? in cm
A = π R²
Diameter = 1mm => Radius = 1/2 mm = 0.5mm = 5 × 10⁻² cm
A = 3.14 × (5 × 10⁻²)² = 78.5 × 10⁻⁴ cm²
ρ for Iron = 10 μ Ω-cm = 10 × 10⁻⁶ Ω-cm
ρ for constantan = 49 μ Ω-cm = 49 × 10⁻⁶ Ω-cm
R iron = R1 = 10 × 10⁻⁶ × L / 78.5 × 10⁻⁴ = L/785 Ω
R constantan = R2 = 49 × 10⁻⁶ × L / 78.5 × 10⁻⁴ = 49L/7850 Ω
R1 & R2 in parallel give 2 Ω
1/R1 + 1/R2 = 1/2
=> 785/L + 7850/49L = 1/2
multiplying both sides by 98L
=> 98 * 785 + 7850*2 = 49L
=> 49L = 785 * (98 + 20)
=> 49L = 785 * 118
=> L = 1890.4 cm
=> L = 18.9 m