Back EMF in DC Motor

In a DC motor, when the armature rotates under the influence of the driving torque, the armature conductors move through the magnetic field, and therefore an EMF is induced in them by the generator action. This induced EMF in the armature conductors acts in opposite direction to the applied voltage $\mathit{V_{s}}$ and is known as the back EMF or counter EMF.

The magnitude of the back EMF is given by,

$$\mathrm{\mathit{E_{b}}\:=\:\frac{\mathit{NP\phi Z}}{\mathrm{60}\mathit{A}}\:\cdot \cdot \cdot (1)}$$

The back EMF $\mathit{E_{b}}$ is always less than the applied voltage $\mathit{V_{s}}$. However, this difference is small when the DC motor is running under normal conditions.

In DC motors, the back EMF $\mathit{E_{b}}$ induced in the armature opposes the applied voltage, thus the applied voltage has to overcome this EMF $\mathit{E_{b}}$ to force a current $\mathit{I_{a}}$ in the armature circuit for motor action. The required power to overcome this opposition is given by,

$$\mathrm{\mathit{P_{m}}\:=\:\mathit{E_{b}I_{a}}\:\cdot \cdot \cdot (2)}$$

The power $\mathit{P_{m}}$ is one which actually converted into mechanical power. For this reason, the power $\mathit{P_{m}}$ is also called as electrical equivalent of mechanical power developed.

Consider a shunt DC motor whose electrical equivalent circuit is shown in Figure-1.

When a DC voltage $\mathit{V_{s}}$ is applied across terminals of the motor, the field electromagnets are excited and armature conductors are supplied with current. Hence, a driving torque acts on the armature which begins to rotate. When the armature rotates, a back EMF is induced in the armature conductors that opposes the applied voltage $\mathit{V_{s}}$. This applied voltage has to force a current through the armature conductors against the back EMF.

The voltage equation of the dc motor can be expressed as,

$$\mathrm{\mathit{V_{s}\:=\:E_{b}+I_{a}R_{a}}\:\cdot \cdot \cdot (3)}$$

Where,$\mathit{R_{a}}$ is the resistance of the armature circuit.

Then, the armature current of the DC motor is given by,

$$\mathrm{\mathit{I_{a}}\:=\:\frac{\mathit{V_{s}-E_{b}}}{\mathit{R_{a}}}\:\cdot \cdot \cdot (4)}$$

Since the applied voltage $\mathit{V_{s}}$ and armature resistance $\mathit{R_{a}}$ are usually fixed for a given motor, then the value of $\mathit{E_{b}}$ will determine the current drawn by the DC motor. If the speed of the DC motor is high, then the value of back EMF is large and hence the motor will draw less armature current and vice-versa.

Significance of Back EMF in DC Motor

The back EMF in a DC motor makes it a self-regulating machine, which means it makes the motor to draw a sufficient amount of armature current to develop the torque required by the mechanical load.

Now, from Equation-4, we may explain the importance of back EMF in the DC motor as −

Case 1 − Motor running on no load

In this case, the dc motor requires a small torque to overcome the frictional and windage losses. Thus, the armature current $\mathit{I_{a}}$ drawn by the motor is small and the back EMF is nearly equal to the supply voltage.

Case 2 − Motor load is changed suddenly

In this case, when load is suddenly attached to the motor shaft, the armature slows down. Consequently, the speed at which the armature conductors move through the magnetic field is decreased and hence the back EMF decreases. This decreased back EMF allows a larger current to pass through the armature conductors, and larger armature current means high driving torque. Hence, it is clear that the driving torque increases as the motor speed decreases. The reduction in motor speed stops when the armature current is sufficient to produce the increased torque required by the mechanical load.

Consider another situation, where the load on the motor is decreased. In this case, the driving torque is momentarily more than the requirement so that the armature is accelerated. The increase in the armature speed increases the back EMF, and causes the armature current to decrease. Once the armature current is just sufficient to produce the reduced driving torque required by the load, the motor will stop accelerating.

This discussion clears that the back EMF in a dc motor automatically regulates the flow of armature current to meet the load requirements.