Transformer Copper Loss
Pcu = Ip² Rp + Is² Rs
Quick answer
This calculator solves Pcu = Ip² × Rp + Is² × Rs for Copper Loss. With Primary Current 2 A, Primary Resistance 0.47 kΩ, Secondary Current 4.4 A, Secondary Resistance 1.03 kΩ, the result is 21.82 kW. It solves in 5 directions, so you can enter the values you have and get the one you need.
Calculator
Formula
Description
Copper (I²R) loss is the heat dissipated in the resistance of the transformer windings as load current flows. It is the load-dependent part of transformer loss: at full load it dominates, and at no load it is essentially zero. Because it grows with the square of current, it sets the transformer’s thermal limit and efficiency at high load.
Variables
- Pcu — Total copper loss (W)
- Ip — Primary RMS current (A)
- Rp — Primary winding resistance (Ω)
- Is — Secondary RMS current (A)
- Rs — Secondary winding resistance (Ω)
Practical Notes
Copper loss is measured by the short-circuit test. Combined with the no-load (iron) loss it gives total loss; maximum efficiency occurs where copper loss equals iron loss.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| Pcu | Copper Loss | W | µW, mW, W, kW |
| Ip | Primary Current | A | pA, nA, µA, mA, A, kA |
| Rp | Primary Resistance | Ω | mΩ, Ω, kΩ, MΩ |
| Is | Secondary Current | A | pA, nA, µA, mA, A, kA |
| Rs | Secondary Resistance | Ω | mΩ, Ω, kΩ, MΩ |
Step by step
- 1. What you know: Primary Current 2 A, Primary Resistance 0.47 kΩ, Secondary Current 4.4 A, Secondary Resistance 1.03 kΩ
- 2. The relation: Pcu = Ip² × Rp + Is² × Rs
- 3. Substitute: Ip = 2 A, Rp = 0.47 kΩ, Is = 4.4 A, Rs = 1.03 kΩ
- 4. Result: Copper Loss = 21.82 kW
Related quantities from the same inputs
- P = I² × R = 1.88 kW
Worked examples
Minimum range
Given: Primary Current 2 mA, Primary Resistance 1 Ω, Secondary Current 4.4 mA, Secondary Resistance 2.2 Ω
Result: Copper Loss = 46.59 µW
Low range
Given: Primary Current 20 mA, Primary Resistance 10 Ω, Secondary Current 44 mA, Secondary Resistance 22 Ω
Result: Copper Loss = 46.59 mW
Typical
Given: Primary Current 2 A, Primary Resistance 0.47 kΩ, Secondary Current 4.4 A, Secondary Resistance 1.03 kΩ
Result: Copper Loss = 21.82 kW
High range
Given: Primary Current 100 A, Primary Resistance 4.7 kΩ, Secondary Current 0.22 kA, Secondary Resistance 10.3 kΩ
Result: Copper Loss = 545500 kW
Maximum range
Given: Primary Current 1 kA, Primary Resistance 47 kΩ, Secondary Current 2.2 kA, Secondary Resistance 103 kΩ
Result: Copper Loss = 5.46 × 10⁸ kW
Solving for each variable
Solve for Copper Loss
Primary Current 2 mA, Primary Resistance 1 Ω, Secondary Current 4.4 mA, Secondary Resistance 2.2 Ω → 46.59 µW
Solve for Primary Resistance
Copper Loss 10 mW, Primary Current 2 mA, Secondary Current 4.4 mA, Secondary Resistance 2.2 Ω → 2.489 kΩ
Solve for Secondary Resistance
Copper Loss 10 mW, Primary Current 2 mA, Primary Resistance 1 Ω, Secondary Current 4.4 mA → 0.5163 kΩ
Solve for Primary Current
Copper Loss 10 mW, Primary Resistance 1 Ω, Secondary Current 4.4 mA, Secondary Resistance 2.2 Ω → 99.79 mA
Solve for Secondary Current
Copper Loss 10 mW, Primary Current 2 mA, Primary Resistance 1 Ω, Secondary Resistance 2.2 Ω → 67.41 mA
How Copper Loss changes with Primary Current
| Primary Current (input) | Copper Loss (result) |
|---|---|
| 0.2 A | 19.96 kW |
| 0.5 A | 20.06 kW |
| 1 A | 20.41 kW |
| 1.5 A | 21 kW |
| 2 A | 21.82 kW |
| 3 A | 24.17 kW |
| 4 A | 27.46 kW |
| 8 A | 50.02 kW |
| 14 A | 112.1 kW |
| 20 A | 207.9 kW |
The same result in other units
| Unit | Value |
|---|---|
| W | 21820 |
| kW | 21.82 |
Embed this calculator
Paste this into any page. It keeps working when this page updates, and credits the source.
<iframe src="https://vbatpower.com/embed/transformer-copper-loss/" width="100%" height="460" style="border:1px solid #1f2a37;border-radius:12px" loading="lazy" title="Transformer Copper Loss"></iframe>
<p><a href="https://vbatpower.com/formulas/transformer-copper-loss/">Transformer Copper Loss</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Transformer Copper Loss?
Use Pcu = Ip² × Rp + Is² × Rs. With Primary Current 2 A, Primary Resistance 0.47 kΩ, Secondary Current 4.4 A, Secondary Resistance 1.03 kΩ, Copper Loss works out to 21.82 kW.
What is the formula for Transformer Copper Loss?
The formula is Pcu = Ip² × Rp + Is² × Rs. Copper (I²R) loss is the heat dissipated in the resistance of the transformer windings as load current flows.
How do you find Primary Resistance when you know the other values?
Rearrange for Primary Resistance: with Copper Loss 10 mW, Primary Current 2 mA, Secondary Current 4.4 mA, Secondary Resistance 2.2 Ω, Primary Resistance is 2.489 kΩ.
How do you find Secondary Resistance when you know the other values?
Rearrange for Secondary Resistance: with Copper Loss 10 mW, Primary Current 2 mA, Primary Resistance 1 Ω, Secondary Current 4.4 mA, Secondary Resistance is 0.5163 kΩ.
What units does Transformer Copper Loss use?
Copper Loss is shown in W, kW. Values are held in SI base units internally, so you can mix prefixes without converting by hand.
Related Concepts
All Magnetics & Transformers formulas →Need more features?
Save calculations, import telemetry data, simulate battery discharge, and collaborate with your team.
Try the App