03 — Calculators
Calculate cable resistance
Cable resistance sits behind almost every other calculation: behind voltage drop, behind power loss, behind loop impedance. The tabulated figure applies at 20 °C — in service the conductor is warmer, and the difference is not a rounding error.
Result
- Resistance at operating temperature
- —Ω
- Resistance at 20 °C
- —Ω
- Loop resistance (out and back)
- —Ω
- Increase due to heating
- —%
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- Opens the print dialog. Choose “Save as PDF” as the destination.
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A guide, not a design to standard. We give no warranty for the correctness of the results, the applicable standards and case-by-case verification govern.
Worked example
The default case the calculator starts with, worked through once. Change the values above and it recalculates immediately.
Inputs
- One-way cable length
- 45 m
- Conductor cross-section
- 6 mm²
- Conductor material
- Copper (κ = 56 m/Ω·mm²)
- Conductor temperature
- 70 °C
Result
- Resistance at operating temperature
- 0.16 Ω
- Resistance at 20 °C
- 0.134 Ω
- Loop resistance (out and back)
- 0.32 Ω
- Increase due to heating
- 19.6 %
Formula
- R₂₀ = L / (κ · A)
- R(ϑ) = R₂₀ · [1 + α · (ϑ − 20 °C)]
- α = 0.00393 /K for copper, 0.00403 /K for aluminium
- Loop resistance = 2 · R(ϑ)
Assumptions and standards
- κ = 56 m/(Ω·mm²) for copper, 35 m/(Ω·mm²) for aluminium at 20 °C.
- Pure resistance. The inductive component is not included and becomes noticeable from about 50 mm² upwards.
- The loop resistance assumes outgoing and return conductors of equal cross-section. With a smaller protective conductor it is larger.
Frequently asked
Which conductor temperature should I use?
For PVC insulation the permissible operating temperature is 70 °C, for cross-linked polyethylene 90 °C. Calculating at full load means using those. For the actual state of a lightly loaded cable, 30 to 40 °C is closer.
Why is the difference between 20 °C and 70 °C so large?
Resistance rises by roughly 0.4 percent per kelvin. Over 50 kelvin that is about 20 percent. A voltage drop that just passes at 20 °C exceeds the limit at operating temperature.
What do I need the loop resistance for?
For the disconnection condition: the short-circuit current at the end of the cable follows from the voltage and the impedance of the loop. If it is too small, the protective device will not disconnect within the required time.
Calculating is the easy part.
A formula gives you a number. Designing a plant also demands installation method, grouping, discrimination, the standards in force and a look at the installed base. That is what we take on.
More tools
- 01Cable cross-section
- 02Voltage drop
- 04Cable losses
- 05Maximum cable length
- 06Current-carrying capacity
- 07Parallel cables
- 08Conductor temperature
- 09Cable capacitance
- 10Short-circuit current
- 11Cable impedance
- 12Network impedance
- 13Short-circuit current at the far end
- 14Thermal short-circuit withstand
- 15Length and disconnection
- 16Motor current
- 17Torque
- 18Starting current
- 19Star-delta starting
- 20Soft starting
- 21Motor efficiency
- 22Speed control instead of throttling
- 23Speed and slip
- 24Setting the motor protection
- 25Single-phase motor
- 26Motor feeder
- 27Required motor rating
- 28PFD and SIL
- 29PFH and SIL
- 30Protective conductor size
- 31Earth rod
- 32Touch voltage
- 33Residual current protection
- 34Check discrimination
- 35Connecting a surge arrester
- 36Enclosure cooling
- 37Reference designation
- 38Reactive power compensation
Contact
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