# Why does a DC motor spin when there is no load applied to it?

So this is a characteristic of a DC motor:

When armature current=0, apparently it still spins quite fast. From what I know, a magnetic field causes a mechanical force on a conductor only when there is current going through the conductor. And in this situation there is no current. So why does it spin?

• Obviously a DC motor with no current applied does not spin, or rather does not accelerate but slowly loses speed to internal friction; so the graph is an oversimplification which cannot be used at zero. – pjc50 Oct 15 '17 at 16:09

If we keep increasing the speed the motor will switch from motoring to generating. At a certain shaft speed the armature current will be zero.

simulate this circuit – Schematic created using CircuitLab

Figure 1. The enhanced speed vs armature current graph.

When armature current=0, apparently it still spins quite fast.

No, it is saying that if the shaft is spinning at a certain speed then the armature current will fall to zero. e.g. A DC motor on a bike might draw zero current at 25 kph. Above 25 kph it will feed power back into the battery.

On a level road the motor might settle down at 20 kph and a certain current as the power in matches wind and rolling resistance. On a slight down-hill the speed will increase through the zero current point and if the bike continues to accelerate the current direction will reverse and go increasingly negative as the speed goes past the rated speed.

From what I know, a magnetic field causes a mechanical force on a conductor only when there is current going through the conductor. And in this situation there is no current. So why does it spin?

It spins because something else can be driving the motor shaft. This happens in many situations such as lifts, hoists, bikes, cars, trains, etc., where the load on the motor changes sign due to gravity.

simulate this circuit

Figure 2. Speed vs armature current for the bike example.

DC motors have three characteristics. (Well more than that but these three matter here.)

1. Back EMF. That is, the motor generates a voltage across it's terminals that opposes the applied voltage. The back EMF is proportional to the rate it is turning.

2. Torque Constant. The amount of torque a motor generates is proportional to the current taken.

3. The current taken by a motor = (Applied voltage - Back-EMF)/coil resistance

What that means is....

If you have a motor with no load, no friction even, it will accelerate till the back EMF voltage matches the applied terminal voltage. At that point there is no current flowing since there is no difference in voltage.

In reality there is friction in the motor plus whatever load is applied to the shaft. The motor will settle at a speed where the current taken creates exactly the amount of torque that balances the load.

$= \huge\frac{V_{Terminal} - (Load /Torque Constant) * Coil Resistance}{Back EMF Constant}$

If the load is too high, the motor will stall.

• I find "back EMF" to be misleading. For an ideal DC motor (i.e., one with no internal resistance or inductance), the voltage across its terminals is proportional to the speed at which it is turning, and the current is proportional to the torque. Adding the word "back" doesn't help my understanding. If you connect the motor to a 3V power supply for example, then it will spin up to whatever speed corresponds to 3V, and after that, if it is unloaded, then no current will flow. IMO, saying that the reason no current flows is because it "generates" 3V of "back EMF" only complicates the picture. – Solomon Slow Oct 15 '17 at 21:16
• @jameslarge no it doesn't. BackEMF is the correct term. Once the BackEMF equals the voltage source no current will flow as there is no voltage difference. With no current there is torque. Without torque there is no acceleration THUS the velocity stabalises – JonRB Oct 15 '17 at 23:00

It spins because there is torque.

There are three equations to consider here

$T = K_t I$.
$V_{bemf} = K_e \omega$

$T = J \ddot{\Theta}$

Likewise:

$V_{batt} = IR + K_e \omega$

A torque applied to an object will accelerate. There is no such thing as an unloaded motor as there is always bearing losses, but that aside As long as there is a positive torque the rotor will accelerate. As long as current can be pushed into the motor, torque will be generated. As long as the voltage source is higher than the backEMF, current can be forced around the stator

• It spins because there is enough torque to overcome the friction in the system. If there was no friction (think of a satellite, spinning in Earth orbit), a spinning object would not need any torque in order to keep spinning. – Solomon Slow Oct 15 '17 at 22:00
• it maintains its velocity because the provided torque overcomes any system load. If there is no load then it doesn't need an torque production to overcome it. I was stating what was needed to reach a velocity. The OP was querying once it is there. To maintain a velocity at 0A is more a graph extrapolation. – JonRB Oct 15 '17 at 23:03