---
title: "Power ratio of two resistors at 70°C"
subject: "Basic Electrical Engineering"
chapter: 1
key: "semester_1/basic_electrical_engineering:two-resistors-temp-coeff-power-ratio"
source: https://www.bctengineer.com/q/semester_1/basic_electrical_engineering/two-resistors-temp-coeff-power-ratio
site: BCT Engineering
---

# Power ratio of two resistors at 70°C

Basic Electrical Engineering · Chapter 1: General Electric System

- Asked in: 2070 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/two-resistors-temp-coeff-power-ratio
- Whole chapter: https://www.bctengineer.com/md/semester_1/basic_electrical_engineering/chapter-1

## Question

Two resistors made of different materials having temperature coefficients of resistance α1 = 0.004/°C and α2 = 0.005/°C are connected in parallel and consume equal power at 15°C. What is the rate of power consumed in resistance R2 to that in R1 at 70°C?

## Short answer

At 15°C resistances are equal. At 70°C, R1 = 1.220R, R2 = 1.275R. Since P ∝ 1/R, P2/P1 = 1.22/1.275 ≈ 0.957.

## Answer

Resistors in parallel have the same voltage. Equal power at 15°C therefore means equal resistance at 15°C: P = V²/R.

#### Step 1: Resistances at 70°C
Let R₁ = R₂ = R at 15°C (α values are taken at 15°C).

R₁(70) = R [1 + 0.004 × (70 − 15)] = 1.220 R
R₂(70) = R [1 + 0.005 × (70 − 15)] = 1.275 R

#### Step 2: Power ratio
At the same voltage, P ∝ 1/R.

P₂/P₁ = R₁/R₂ = 1.220/1.275 = 0.957

**Answer: P₂ : P₁ ≈ 0.957 (R₂ consumes about 4.3 % less power than R₁)**

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. Two parallel resistors consume equal power at 15 degC. What follows?
   A. Their resistances are equal at 15 degC
   B. Their alphas are equal
   C. Their currents differ
   D. Their resistances differ by the ratio of alphas
   Answer: A. Same voltage and P = V^2/R, so equal power means equal resistance. (Key point: Equal power in parallel)

2. At 70 degC the resistances are:
   A. R1 = 1.275 R, R2 = 1.220 R
   B. R1 = 1.004 R, R2 = 1.005 R
   C. R1 = 1.220 R, R2 = 1.275 R
   D. R1 = 1.28 R, R2 = 1.35 R
   Answer: C. R1 = R(1 + 0.004 x 55) = 1.220 R; R2 = R(1 + 0.005 x 55) = 1.275 R. (Key point: Resistances at 70 degC)

3. P2/P1 at 70 degC equals:
   A. 1.275/1.220 = 1.045
   B. R1/R2 = 1.220/1.275 = 0.957
   C. 1
   D. 0.5
   Answer: B. At equal voltage P is proportional to 1/R, so P2/P1 = R1/R2 = 0.957. (Key point: Power ratio)

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