--- title: "Copper and iron conductors current ratio" subject: "Basic Electrical Engineering" chapter: 1 key: "semester_1/basic_electrical_engineering:copper-iron-parallel-current-division" source: https://www.bctengineer.com/q/semester_1/basic_electrical_engineering/copper-iron-parallel-current-division site: BCT Engineering --- # Copper and iron conductors current ratio Basic Electrical Engineering · Chapter 1: General Electric System - Asked in: 2073 Chaitra, 6 marks - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_1/basic_electrical_engineering/copper-iron-parallel-current-division - Whole chapter: https://www.bctengineer.com/md/semester_1/basic_electrical_engineering/chapter-1 ## Question Two conductors, one of copper and the other of iron are connected in parallel and at 20°C carry equal currents. What proportion of current will pass through each, if the temperature is raised to 100 °C? Assume temperature coefficient of resistance at 20 °C for copper as 0.0042 per °C and for iron as 0.006 per °C. ## Short answer At 20°C resistances are equal. At 100°C: R_copper = 1.336R, R_iron = 1.480R. Since parallel voltage is same, current division is inverse: I_copper/I_iron = 1.480/1.336 = 1.108. Copper carries 52.6% and iron 47.4% of total current. ## Answer Two conductors in parallel have the same voltage across them, so the currents divide in inverse ratio of their resistances: I₁/I₂ = R₂/R₁. #### Step 1: Equal currents at 20°C Equal currents at the same voltage means equal resistances at 20°C. Let R_cu = R_fe = R at 20°C. #### Step 2: Resistances at 100°C R_cu = R [1 + 0.0042 × (100 − 20)] = R × 1.336 R_fe = R [1 + 0.006 × (100 − 20)] = R × 1.480 #### Step 3: Current division I_cu/I_fe = R_fe/R_cu = 1.480/1.336 = 1.108 Fraction through copper = 1.480/(1.336 + 1.480) = 0.5256 Fraction through iron = 1.336/(1.336 + 1.480) = 0.4744 **Answer: Copper carries about 52.6 % and iron about 47.4 % of the total current (ratio 1.108 : 1).** ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Two parallel conductors carry equal currents at 20 degC. What does this tell us? A. They have equal resistances at 20 degC B. They have equal temperature coefficients C. They have equal voltages only at 100 degC D. Copper has twice the resistance of iron Answer: A. Same voltage and same current means R_cu = R_fe at 20 degC. (Key point: Equal currents imply equal resistance) 2. What are the multipliers on the 20 degC resistance at 100 degC? A. Cu 1.42, Fe 1.60 B. Cu 1.336, Fe 1.480 C. Cu 1.0042, Fe 1.006 D. Cu 1.480, Fe 1.336 Answer: B. Cu: 1 + 0.0042 x 80 = 1.336; Fe: 1 + 0.006 x 80 = 1.480. (Key point: Resistances at 100 degC) 3. In parallel, the current in each branch is proportional to: A. Its resistance B. Its temperature coefficient C. The square of its resistance D. The reciprocal of its resistance Answer: D. Same voltage across both gives I proportional to 1/R, so I_cu/I_fe = R_fe/R_cu. (Key point: Current division rule) 4. What fraction of the total current passes through copper at 100 degC? A. About 47.4 % B. About 50 % C. About 52.6 % D. About 60 % Answer: C. Fraction = 1.480/(1.336 + 1.480) = 0.5256 because copper has the lower resistance. 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