Motor Current⚠ unverified
Electrical / Motors · Compute the armature current of a DC motor
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| V | V | V | 1.0 | Terminal (supply) voltage |
| R | R | — | 1.0 | Armature resistance |
| back_emf | backemf | V | 1.0 | Back electromotive force |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| result | I | A | Armature current, in amperes (A). Returns 0.0 when ``R`` is not positive |
The science & history
Understanding the Parameters
- $V$ — the driving voltage.
- $E$ — the back‑EMF, $E = K_e\omega$, which grows with speed and subtracts from $V$.
- $R$ — the (small) armature‑winding resistance; because it is small, even a modest net voltage $V-E$ drives a large current, which is why start‑up inrush is severe.
Derivation (Approaching a Proof)
Apply Kirchhoff's voltage law around the armature loop. The supply voltage is dropped across the winding resistance plus the back‑EMF source:
$$V = IR + E \quad\Rightarrow\quad I = \frac{V - E}{R}.$$
At standstill $E = 0$, so $I = V/R$ — a large inrush limited only by the small $R$ (hence soft‑start resistors or current limiting). As the motor accelerates, $E = K_e\omega$ rises, the net voltage $V-E$ shrinks, and the current falls until torque ($T = K_t I$, see Torque Constant) just balances the load. This negative feedback is what gives a DC motor its stable, self‑regulating speed.
History
The relation is Ohm's law applied to the armature circuit with Faraday's back‑EMF included — a synthesis that dates to the development of practical DC machines in the late 19th century and underlies every motor starter and drive since.
Related Concepts: Back Emf, Ohm's Law solve for current, Torque Constant, Motor Efficiency
Notes: Registry calculator motor-current (unverified; $R$ mislabelled dimensionless — should be
ohms). Steady/instantaneous armature model; neglects inductance transients and brush drop.