Back Emf

The reason why electromagnetic generators produce AC voltage is that the turning wire loop has the magnetic flux going through its cross section in opposite directions every half turn.

Using the concept of induction, we can also answer a question you may have had when we discussed motors and electromagnets: if you connect a solenoid (or coil) directly to a battery, isn't that just a short circuit that will drain the battery really quickly? For an electromagnet operating with DC current, that is indeed a problem, so we have to limit the current it can draw from the battery (e.g. using resistors). But in a motor, the coil does not act the same way. It does not drain the battery even if connected directly to it.

The difference is that the coil in the motor does not see a supply of continuous direct current while it is turning. To keep the rotation going, the current through the coil is reversed every half turn, so there is, in fact, an alternating current in the rotating coil. Now we know that any current produces a magnetic field, and that makes the motor into an electromagnet.

However, unlike the DC electromagnet, we are now dealing with a magnet whose magnetic field is constantly changing. And according to Faraday's Law, this changing field will in turn cause magnetic induction – leading to an emf. But what is the loop in which this emf will appear? It is the same coil that produced the changing magnetic field in the first place. So any electromagnet whose current is changing will produce an emf inside of itself!

Read this text, which explains how Lenz's Law dictates the direction of the induced emf and always opposes the voltage applied to the coil to get the current going in the first place. What does this means for a motor coil? As soon as it starts rotating, it will not act like a short circuit anymore because it will oppose the varying current flowing through it.

It has been noted that motors and generators are very similar. Generators convert mechanical energy into electrical energy, whereas motors convert electrical energy into mechanical energy. Furthermore, motors and generators have the same construction. When the coil of a motor is turned, magnetic flux changes, and an emf (consistent with Faraday’s law of induction) is induced.

The motor thus acts as a generator whenever its coil rotates. This will happen whether the shaft is turned by an external input, like a belt drive, or by the action of the motor itself. That is, when a motor is doing work and its shaft is turning, an emf is generated. Lenz’s law tells us the emf opposes any change, so that the input emf that powers the motor will be opposed by the motor’s self-generated emf, called the back emf of the motor. (See Figure 23.25.)


Figure shows an electric circuit. The circuit has a cell represented as driving e m f of voltage one hundred and twenty volt is connected in series with a variable e m f source with a range of voltage from zero to one hundred twenty volts and a resistance R. The other end of resistance R is connected to an open switch. The switch is connected back to the Driving e m f cell.

Figure 23.25 The coil of a DC motor is represented as a resistor in this schematic. The back emf is represented as a variable emf that opposes the one driving the motor. Back emf is zero when the motor is not turning, and it increases proportionally to the motor’s angular velocity.


Back emf is the generator output of a motor, and so it is proportional to the motor’s angular velocity \omega . It is zero when the motor is first turned on, meaning that the coil receives the full driving voltage and the motor draws maximum current when it is on but not turning. As the motor turns faster and faster, the back emf grows, always opposing the driving emf, and reduces the voltage across the coil and the amount of current it draws. This effect is noticeable in a number of situations.

When a vacuum cleaner, refrigerator, or washing machine is first turned on, lights in the same circuit dim briefly due to the IR drop produced in feeder lines by the large current drawn by the motor. When a motor first comes on, it draws more current than when it runs at its normal operating speed. When a mechanical load is placed on the motor, like an electric wheelchair going up a hill, the motor slows, the back emf drops, more current flows, and more work can be done. If the motor runs at too low a speed, the larger current can overheat it (via resistive power in the coil, P=I^{2}R), perhaps even burning it out. On the other hand, if there is no mechanical load on the motor, it will increase its angular velocity \omega until the back emf is nearly equal to the driving emf. Then the motor uses only enough energy to overcome friction.

Consider, for example, the motor coils represented in Figure 23.25. The coils have a 0.400 \Omega\: equivalent resistance and are driven by a 48.0\: V emf. Shortly after being turned on, they draw a current I=V/R=(48.0\: V)/(0.400\: \Omega)=120\:A and, thus, dissipate P=I^{2}R=5.76\: kW of energy as heat transfer. Under normal operating conditions for this motor, suppose the back emf is 40.0\: V. Then at operating speed, the total voltage across the coils is 8.0\: V (48.0\: V minus the 40.0\: V back emf), and the current drawn is I=V/R=(8.0\: V)/(0.400\: \Omega)=20\: A. Under normal load, then, the power dissipated is P=IV=(20\: A)/(8.0\: V)=160\: W. The latter will not cause a problem for this motor, whereas the former 5.76\: kW would burn out the coils if sustained.

 


Source: Rice University, https://openstax.org/books/college-physics/pages/23-6-back-emf
This work is licensed under a Creative Commons Attribution 4.0 License.

Last modified: Tuesday, August 31, 2021, 4:15 PM