varying load from electric motor
A motor can be modeled as a resistor, inductor, and voltage source in series. Your power source is probably a (probably variable) voltage source:







simulate this circuit &ndash; Schematic created using CircuitLab

The current through \$L_m\$ is what makes the motor go. The magnetic field in this inductance is what creates the torque in the motor. More current = stronger field = more torque.

\$V_m\$ is the voltage created by the rotor moving through the stator's magnetic field, by Faraday's law of induction. The faster the motor is spinning, the higher \$V_m\$ will be.

\$R_m\$ is the resistance of the windings. It is usually small, and desirably so, since it represents a loss that does nothing but make heat.

Say the vehicle is already moving fast. Since the current in the motor is constant, the voltage across \$L_m\$ is \$0V\$. We can consider it to be a short. Thus by Kirchoff's voltage law:

$$ V_{bat} - V_{Rm} - V_m = 0 $$

\$V_{Rm}\$ will be small, because there's not much current, because there's not much torque (just enough to overcome friction). So \$V_m\$ must be very close to \$V_{bat}\$, which makes sense, if the vehicle is already moving fast, and \$V_{bat}\$ is proportional to speed. This is why not much current is drawn from the battery when the vehicle is at a constant speed.

But, what if the vehicle isn't moving, but we apply the same voltage to the motor?

In this case, \$V_m\$ is zero, because the motor isn't turning. Initially, the current will be \$0A\$, but soon, it will rise to some maximum value limited only by \$R_m\$. At this point the current (and torque) are at the maximum. And let's say the rotor can't turn; it's locked in place. This is the stall current of the motor, when the full supply voltage is dropped over \$R_m\$, the current isn't changing (\$V_{Lm} = 0V\$) and the rotor isn't turning (\$V_m = 0V\$). Essentially, the battery is shorted by just a small resistor, \$R_m\$.

If the rotor isn't locked, that huge torque from the huge current will cause the motor to accelerate. (Torque is a rotating force, and force is the product of mass and acceleration: \$F=ma\$, but also \$a=F/m\$. If the torque does not exactly balance friction, there will be a force, and there must be acceleration). \$V_m\$ will become greater, thus reducing the voltage seen by \$L_m\$ and \$R_m\$, thus decreasing the current, until the vehicle has accelerated so much that the torque is just enough to balance friction (there is no net force), and the acceleration stops.

Here's an interesting consequence: If \$R_m = 0\Omega\$, and also \$V_{bat}\$ is an ideal voltage source, and also the wires are ideal, then the speed regulation of the motor is perfect. That is, if you put a brake on it, the motor's torque (and, the current drawn from \$V_{bat}\$) will increase exactly enough to maintain the same speed. Or, if you increase \$V_{bat}\$, this will result in an infinite torque, which will accelerate your vehicle instantly to the new speed at which \$V_m = V_{bat}\$. This is because with no resistance to otherwise limit the current, any difference between \$V_m\$ and \$V_{bat}\$ results in an infinite current (at least eventually; \$\frac{di}{dt}\$ is still limited by \$L_m\$).