Calculate the induced back EMF E of a running DC motor from armature voltage, armature current and armature-circuit resistance using E = U − IA·RA. In motoring operation the terminal voltage divides into back EMF and the resistive armature drop.
Select a target and calculate.
E = U − IA·RA falls linearly with the armature current, i.e. with load. The gap to the dashed supply voltage U is the drop across the armature resistance; at E = 0 the motor is at standstill (starting current U/RA).
Calculate the induced back EMF E of a running DC motor from armature voltage, armature current and armature-circuit resistance using E = U − IA·RA. In motoring operation the terminal voltage divides into back EMF and the resistive armature drop.
U=230 V, IA=20 A and RA=0.5 Ω give 10 V armature drop, E=220 V and Pconv=4.4 kW.
Steady motoring with constant flux and negligible armature inductance; brush drop, mechanical losses and field power are excluded.
This calculator separates resistive armature drop from speed-induced back EMF in a running DC motor, revealing the share of electrical input converted electromagnetically.
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.
E = U − IA·RAPconv = 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. |
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.
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.
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.
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.
Motor test-bench evaluation, steady-state plausibility checks and teaching electromechanical energy conversion.
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.
Motor test-bench evaluation, steady-state plausibility checks and teaching electromechanical energy conversion.
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.
Steady linear operation. Armature inductance, commutation/brush drop, magnetic saturation, friction/fan loss and field power are excluded.