---
title: "Nichrome wire size for 5.5 kW resistance oven"
subject: "Utilization of Electrical Energy"
chapter: 5
key: "semester_7/utilization_of_electrical_energy:nichrome-oven-5-5kw-wire-size"
source: https://www.bctengineer.com/q/semester_7/utilization_of_electrical_energy/nichrome-oven-5-5kw-wire-size
site: BCT Engineering
---

# Nichrome wire size for 5.5 kW resistance oven

Utilization of Electrical Energy · Chapter 5: Electric Heating

- Asked in: 2080 Bhadra, 8 marks
- Video: [ELECTRICAL HEATING  - PART - 03 - THREE PROBLEMS IN DESIGN OF HEATING ELEMENT](https://www.youtube.com/watch?v=4tFLfZXrAeM) — zenmurali Sachithanandam
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_7/utilization_of_electrical_energy/nichrome-oven-5-5kw-wire-size
- Whole chapter: https://www.bctengineer.com/md/semester_7/utilization_of_electrical_energy/chapter-5

## Question

A 5.5 kW, 220 V, and 1-ϕ resistance oven is to have nichrome wire heating elements. If the wire temperature is to be 1100°C and that of the charges 500°C. Estimate the diameter and length of the wire. The resistivity of the nichrome alloy is 42.5 μΩ-m. Assume the radiating efficiency and the emissivity of the element as 1.0 and 0.9 respectively.

## Short answer

Use R = V²/P = 8.8 ohm and heat dissipation H = 1.6456×10⁵ W/m². Solving resistance and radiation conditions gives diameter about 4.03 mm and length about 2.64 m.

## Answer

The wire must give 5.5 kW at 220 V (resistance condition) and must radiate this power at 1100°C (surface condition).

**Given:** $P = 5500$ W, $V = 220$ V, $T_1 = 1100 + 273 = 1373$ K, $T_2 = 500 + 273 = 773$ K, $\rho = 42.5 \times 10^{-6}\ \Omega$m (as given), $k = 1.0$, $e = 0.9$.

#### Heat dissipated per m² of wire surface
$$
\begin{aligned}
H &= 5.72\,e\,k\left[\left(\frac{T_1}{100}\right)^4 - \left(\frac{T_2}{100}\right)^4\right] \\
&= 5.72 \times 0.9 \times 1.0 \times (13.73^4 - 7.73^4) \\
&= 5.148 \times (35\,537 - 3\,570) = 1.6456 \times 10^5\ \text{W/m}^2
\end{aligned}
$$

#### Resistance condition
$$
R = \frac{V^2}{P} = \frac{220^2}{5500} = 8.8\ \Omega
$$
$$
R = \frac{\rho l}{\pi d^2/4} \Rightarrow \frac{l}{d^2} = \frac{\pi R}{4\rho} = \frac{\pi \times 8.8}{4 \times 42.5 \times 10^{-6}} = 1.6262 \times 10^5 \quad (1)
$$

#### Surface (heat) condition
$$
P = (\pi d l)H \Rightarrow d\,l = \frac{5500}{\pi \times 1.6456\times10^5} = 0.010638 \quad (2)
$$

#### Solving (1) and (2)
$$
\begin{aligned}
d^3 &= \frac{0.010638}{1.6262 \times 10^5} = 6.542 \times 10^{-8} \\
d &= 4.03 \times 10^{-3}\ \text{m} = 4.03\ \text{mm} \\
l &= \frac{0.010638}{4.03 \times 10^{-3}} = 2.64\ \text{m}
\end{aligned}
$$

**Answer:** Wire diameter $\approx 4.03$ mm and length $\approx 2.64$ m.

Note: the resistivity is used as given; real nichrome is about $1.1\ \mu\Omega$m.

## Check yourself

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

1. What resistance must the element have for 5.5 kW at 220 V?
   A. 40 Ω
   B. 8.8 Ω
   C. 0.025 Ω
   D. 220 Ω
   Answer: B. R = V^2/P = 220^2/5500 = 8.8 Ω. (Key point: Resistance of the element)

2. What is the role of H = 5.72 e k [(T1/100)^4 - (T2/100)^4]?
   A. Gives resistance of the wire
   B. Gives wire length directly
   C. Gives heat radiated per m^2 of wire surface
   D. Gives mass of the charge
   Answer: C. H (about 1.65x10^5 W/m^2) is used with P = π d l H. (Key point: Heat per unit surface)

3. Which equation expresses that the wire radiates the full power?
   A. P = π d^2 H/4
   B. P = (π d l) H
   C. P = ρ l / A
   D. P = V I cos(phi)
   Answer: B. Surface area of a round wire is π d l, so P = π d l H gives dl = 0.010638 m^2. (Key point: Surface condition)

4. The solution gives approximately:
   A. d = 4.03 mm, l = 2.64 m
   B. d = 2 mm, l = 10 m
   C. d = 8 mm, l = 1 m
   D. d = 4.03 m, l = 2.64 mm
   Answer: A. d^3 = 6.542x10^-8 gives d = 4.03 mm, and l = 0.010638/d = 2.64 m. (Key point: Final result)

## Close variants set in other exams

- [Nichrome wire size for 4.5 kW resistance oven](https://www.bctengineer.com/question.md?key=semester_7%2Futilization_of_electrical_energy%3Anichrome-oven-4-5kw-wire-size) — Utilization of Electrical Energy, chapter 5, asked 3×

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