Electricity - (Holiday Assignment)
Q1: Two metallic wires A and B of same material are connected in parallel. Wire A has length l and radius r and wire B has length 2l and radius 2r. Compare the ratio of the total resistance of parallel combination and the resistance of wire A.
Answer:
Wire A:
Length = l
Radius = r
Area = πr²
R₁ = ρ x l /(πr²)
Wire B:
Length = 2l
Radius = 2r
Area = π(2r)² = 4πr²
R₂ = ρ x 2l /(4πr²) = ρ x l /(2πr²)
Let Rₚ = effective resistance of parallel combination
∴ 1/Rₚ = 1/R₁ + 1/R₂
1/Rₚ = (πr²)/ρl + (2πr²)/ρl
Rₚ = ρl/(3πr²)