Physics

Physics

Problem

Three metallic segments are welded end-to-end to form a single conductor. The first segment is 20 cm20\,\text{cm} long, made of copper (ρ=1.7×10−8 Ω⋅m\rho = 1.7 \times 10^{-8}\,\Omega\cdot\text{m}) with cross-sectional area 1.0 mm21.0\,\text{mm}^2. The second segment is 30 cm30\,\text{cm} long, made of aluminium (ρ=2.8×10−8 Ω⋅m\rho = 2.8 \times 10^{-8}\,\Omega\cdot\text{m}) with area 1.5 mm21.5\,\text{mm}^2. The third segment is 25 cm25\,\text{cm} long, made of iron (ρ=1.0×10−7 Ω⋅m\rho = 1.0 \times 10^{-7}\,\Omega\cdot\text{m}) with area 0.8 mm20.8\,\text{mm}^2. a. (i) Calculate the resistance of each segment at room temperature. b. (ii) Determine the total resistance of the composite conductor. c. (iii) A potential difference of 5.0 V5.0\,\text{V} is applied across the free ends of the composite conductor. Find the current in the circuit. d. (iv) Compute the potential drop across each individual segment.
Intuitive explanation

When resistors are connected in series, the total resistance is just the sum of individual resistances—and here, each segment's resistance depends on both its material (resistivity ρ\rho) and its geometry (length LL and area AA) through R=ρL/AR = \rho L/A. The key insight is that even though all three segments carry the same current, they have very different resistances because of their different resistivities and cross-sections, so you need to calculate each one separately using the resistance formula, then add them up to find the total.

Intuitive explanation

When resistors are connected in series, the total resistance is just the sum of individual resistances—and here, each segment's resistance depends on both its material (resistivity ρ\rho) and its geometry (length LL and area AA) through R=ρL/AR = \rho L/A. The key insight is that even though all three segments carry the same current, they have very different resistances because of their different resistivities and cross-sections, so you need to calculate each one separately using the resistance formula, then add them up to find the total.

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