Batteries, Machines and Electricity Systems

Why a Brushed DC Motor Starts Differently

Understand commutation, back EMF and starting current.

By MySunDirection
Published 13 October 2026
Updated 14 October 2026
16 min read

One-minute answer

You need to size or verify a real system using “Why a Brushed DC Motor Starts Differently”, with units, duty and limits that match the application.

Explain how brushes and a commutator maintain torque direction, why back EMF grows with speed, and why startup current follows an inductive rise toward a potentially destructive stationary limit.

Select or check first: Define the required outcome, operating conditions and exact component or system boundary before choosing a part or method.
Controlling assumption: Circuit state, waveform, source impedance, ratings, temperature and protection topology match the equipment being analysed.
Top risk: Do not use a deliberate stall as a casual current test. At stall there is no speed-generated back EMF, so copper loss approaches I²R and the commutator, brushes, winding, driver, wiring and source can overheat quickly. Use maker data, a controlled fixture and current limiting. Remove power if expected motion does not begin.
Proof: Check the exact manufacturer data, units and limits, then verify the result by calculation, measurement or a controlled acceptance test.

Start with the basics Optional foundation before “Why a Brushed DC Motor Starts Differently”

Electrical-engineering basics

Electrical behaviour becomes easier to reason about when every voltage has a reference and every current has a complete return path.

Voltage: Voltage is potential difference between two points. A voltage statement is incomplete unless both points or its reference are known.
Current: Current is charge flow through a path. It does not disappear after a component; in a complete circuit it returns to the source.
Resistance and impedance: Resistance opposes steady current. Impedance extends that idea to changing signals and can depend on frequency through capacitance and inductance.
Power and heat: Electrical power is the rate of energy transfer. Some becomes useful output and some becomes heat that must stay within component and enclosure limits.
Rating versus operating point: A rating is a limit or qualified condition, not a target. The operating point must remain inside all relevant voltage, current, power, temperature and timing limits.

How to use this article: Draw the source, load, reference and return path before calculating. Treat exposed or stored electrical energy as hazardous until isolation is proved.

On this page

Mechanical commutation keeps useful torque in the same rotational direction
Rotation creates an opposing voltage
At the first instant current is zero—but its stationary limit can be very high
Design the source and driver for the transient

A brushed permanent-magnet DC motor behaves differently at rest because it is not yet generating the voltage that normally opposes the supply. Brushes and a segmented commutator route current through rotating windings; electromagnetic torque accelerates the rotor; rotation generates back electromotive force; that back EMF reduces the voltage left to drive winding current. Startup therefore couples an electrical transient to mechanical acceleration.

Mechanical commutation keeps useful torque in the same rotational direction

Simplified brushed DC motor at successive half turns, showing brushes and split commutator reversing coil current so electromagnetic torque continues in one rotational direction. — The commutator reverses current in the rotating coil near each half turn so the torque continues to drive the chosen direction.

A single coil would otherwise pass through a position where its torque reverses. The split commutator swaps the coil’s connection to the stationary brushes as the rotor turns. Real motors distribute conductors and commutator segments around the armature to reduce torque ripple and avoid relying on a single dead position. Brush contact drop, wear and sparking are part of the real machine.

Rotation creates an opposing voltage

Brushed DC motor model showing applied voltage, winding resistance, current and speed-proportional back EMF, plus the response to increased mechanical load. — Higher speed produces more back EMF. If load torque rises, the motor slows, back EMF falls, current rises and electromagnetic torque increases until a new operating point or a limit is reached.

Electrical and torque model

V = L·di/dt + R·i + kₑω + V_brush; τ_e ≈ kₜi

The constants and units must come from the motor maker. In a simplified steady state, the inductive term is zero and V − back EMF drives current through resistance. Friction, iron loss, temperature-dependent winding resistance and drive voltage drop shift the actual operating point.

V: motor-terminal voltage, V
L: armature inductance, H
i: armature current, A
R: armature resistance at its present temperature, Ω
kₑ: back-EMF constant in units consistent with angular speed
ω: angular speed, rad/s
V_brush: effective brush-contact drop, V
τ_e: electromagnetic torque, N·m
kₜ: torque constant in consistent units

Follow the feedback inherent in the motor
Event	Immediate change	Result if within limits
Supply is applied at rest	Back EMF is zero; current begins rising through L and R	High torque accelerates the rotor
Speed rises	Back EMF increases	Current falls from the starting region
Mechanical load increases	Speed initially falls	Back EMF falls, allowing more current and torque
Shaft is stalled	Speed and back EMF become zero	Current tends toward a resistance-limited value and heating rises rapidly
Drive limits current	Available torque is capped	Acceleration takes longer or the load may not start

At the first instant current is zero—but its stationary limit can be very high

Qualitative brushed DC motor startup plots showing speed rising from zero, back EMF growing with speed, and current rising inductively before falling as the motor accelerates. — For an initially unenergized winding, inductance prevents an instantaneous current jump. If the rotor stayed still, current would approach the stationary limit; acceleration builds back EMF and usually turns current downward.

Stationary electrical limit

i(t) ≈ (V/R)·(1 − e^(−tR/L)) while ω = 0

This expression assumes constant V, R and L and neglects brush and drive drops. In a successful start, speed is not zero for long: back EMF grows and changes the waveform. A current-limited driver may impose a different ramp or plateau.

i(t): armature current after energization, A
V: constant applied voltage in the simplified model, V
R: total series resistance, Ω
L: armature inductance, H
t: time after application, s

Design the source and driver for the transient

The motor is only one part of the starting system
Check	Failure prevented
Rated and maximum motor voltage	Overspeed, insulation or commutator damage
Startup or stall-current data	Undersized driver, connector, fuse or source
Driver current limit and safe operating area	Switch overstress during acceleration or jam
Source voltage sag	Controller reset and failed acceleration
Load inertia and breakaway torque	A motor that cannot reach the back-EMF region
Duty cycle and cooling	Repeated-start thermal accumulation
Flyback/current recirculation path	Overvoltage when current is switched

Why adding load can raise current even though speed falls

Added load torque initially decelerates the rotor. Lower speed means lower back EMF, leaving more of the applied voltage across the winding resistance and inductance. Current rises, and the torque-current relationship supplies more electromagnetic torque. Equilibrium occurs when motor torque balances load and losses, provided current, voltage and temperature limits are not exceeded.

Use Resistance, Nonlinear Loads and Heat to interpret winding heating, and Follow Energy Through an Electrical System to place the source, converter, driver and motor in one diagnostic chain.

One-minute questions

Questions to answer before you apply this lesson

What should I select or check first for Why a Brushed DC Motor Starts Differently?

Define the required outcome, operating conditions and exact component or system boundary before choosing a part or method.

Which assumption can change the conclusion?

Circuit state, waveform, source impedance, ratings, temperature and protection topology match the equipment being analysed.

What can go wrong if I copy the example directly?

Do not use a deliberate stall as a casual current test. At stall there is no speed-generated back EMF, so copper loss approaches I²R and the commutator, brushes, winding, driver, wiring and source can overheat quickly. Use maker data, a controlled fixture and current limiting. Remove power if expected motion does not begin.

How do I verify the result in the real system?

Check the exact manufacturer data, units and limits, then verify the result by calculation, measurement or a controlled acceptance test.

Sources and further reading

Motor Constantsmaxon Support · 2026-10-13Motor-manufacturer source reviewed for torque/current and back-EMF/speed relationships and unit handling.
Motor Data and Simulationmaxon Support · 2026-10-13Reviewed for the motor electrical model, resistance, inductance, induced voltage and speed-torque interpretation.
Rotating Speed of DC Motor and Counter-Electromotive ForceNidec Corporation · 2026-10-13Motor-manufacturer educational source reviewed for speed-proportional counter EMF and its relationship to torque constant.