Tutoring physics 12, you encounter this concept.  The tutor offers the formula with an explanation.

Induction refers to the creation of voltage in a wire that is not connected to a power source.  It’s the premise that enables generation of electricity.  To induce voltage in a loop of wire, you need to spin it in a magnetic field.  The axis of rotation must be at right angles to the field.  You’ll get induced voltage according to

Emf=-NΔ(BA)/Δt

I’ll be covering the above formula in more detail in future posts, but today the focus is back emf.  Back emf evolves during the operation of an electric motor due to the fact that, once again, a loop of wire is spinning in a magnetic field.  Back emf is so-called because it opposes the line voltage powering the motor.  However, back emf is good, not bad.

Consider the following question:

The resistance of an electric motor is 10.0Ω, while the line voltage is 120V.  At operating speed, the motor draws 2.5A.  What is the back emf?

Solution:

We know that, without considering back emf, I=V/R.  Therefore, the current drawn should be I=120/10.0=12A.  The fact that, at operating speed, the motor draws much less than 12A, is due to back emf.  Specifically,

Back emf=V_line-IR

In our specific case,

Back emf=120 – (2.5)(10.0)=95V

Essentially, as the coils of wire in the motor start to spin in the motor’s magnetic field, they become a generator. The generator opposes the line voltage. In our example, with Back emf=95V, the line voltage is reduced from 120V to 25V in the motor. However, that’s good, because it drastically reduces the motor’s power consumption. Recalling the equation for power, P=I^2R, we see that without back emf, our motor would consume (12)^2(10.0) or 1440 Watts. Because of back emf, it consumes only (2.5)^2(10.0)=62.5W.

The efficiency of an electric motor can be related as

eff=(Back emf)/V_line

By that relationship, our motor above is 95/120 or 79% efficient.

In future posts I’ll be revisiting the concepts touched upon herein:)

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.