Calculation
E = U − IA·RA; Pconv = E·IA
In motoring operation, terminal voltage divides into back EMF and resistive armature drop.
Busch 2006, Abschnitt 8.2.3.1 Ersatzschaltbild
DC motor back EMF
In motoring operation, terminal voltage divides into back EMF and resistive armature drop.
MINTSI
02
Result
Select a target and calculate.
Understand the inputs
- Induced back EMF E — Voltage induced by rotation in the magnetic field, opposing armature current.
- Armature voltage U — Actual DC voltage directly at the armature terminals at the steady operating point.
- Armature current IA — Measured motor current in the armature circuit, excluding separately supplied field current.
- Armature-circuit resistance RA — Hot resistance of armature winding, brushes and permanent connection path at the operating point.
Example
U=230 V, IA=20 A and RA=0.5 Ω give 10 V armature drop, E=220 V and Pconv=4.4 kW.
Assumptions and limits
Steady motoring with constant flux and negligible armature inductance; brush drop, mechanical losses and field power are excluded.
Understand DC motor back EMF
This calculator separates resistive armature drop from speed-induced back EMF in a running DC motor, revealing the share of electrical input converted electromagnetically.
What does this quantity describe?
In steady motoring, U=E+IA·RA. E opposes applied voltage and, at constant field flux, rises with speed. E·IA is converted electromagnetic power before mechanical loss.
Formula and variables
E = U − IA·RA; Pconv = E·IA
E = U−IA·RAPconv = E·IAPcu = IA²·RA
| Symbol / input | Meaning |
|---|---|
| Induced back EMF E | Voltage induced by rotation in the magnetic field, opposing armature current. |
| Armature voltage U | Actual DC voltage directly at the armature terminals at the steady operating point. |
| Armature current IA | Measured motor current in the armature circuit, excluding separately supplied field current. |
| Armature-circuit resistance RA | Hot resistance of armature winding, brushes and permanent connection path at the operating point. |
Choose the inputs correctly
Measure U directly at the armature terminals. IA is armature current only, excluding separately supplied field current. RA must represent hot winding, brush equivalent and permanent connection resistance.
How to use the calculator
Measure U and IA at the same stable operating point and use a temperature-corrected RA where possible. Compare E between points only with known or constant field flux.
Worked example
At 230 V, 20 A and 0.5 Ω, resistive drop is 10 V. Back EMF is 220 V and converted power is 220 V·20 A=4.4 kW.
Understand the result and units
E close to U means a small armature drop. A greater IA·RA share raises IA²·RA copper loss and reduces voltage available for conversion.
U and E are voltages, IA current and RA resistance. Coherent SI values are used even with selected prefix units.
Typical applications
Motor test-bench evaluation, steady-state plausibility checks and teaching electromechanical energy conversion.
Assumptions, limits and common mistakes
Steady linear operation. Armature inductance, commutation/brush drop, magnetic saturation, friction/fan loss and field power are excluded.
Common mistake: Do not use total supply current as IA when the field is connected in parallel. Do not apply cold winding resistance directly to hot operation.
Frequently asked questions
What is “DC motor back EMF” used for?
Motor test-bench evaluation, steady-state plausibility checks and teaching electromechanical energy conversion.
Where do the input values come from?
Measure U directly at the armature terminals. IA is armature current only, excluding separately supplied field current. RA must represent hot winding, brush equivalent and permanent connection resistance.
What does the result not cover?
Steady linear operation. Armature inductance, commutation/brush drop, magnetic saturation, friction/fan loss and field power are excluded.