QUESTIONS IN THE BOX:


6. "Does a back emf produce a heating effect?"

This is not a trivial question! In the sense that the back-emf produced by a changing current in an inductor is a contribution to the total emf in a circuit then, yes, it does have an effect on the power dissipated in a resistor in a circuit. (As an aside, bear in mind that when we talk about inductors in class usually we assume they are "pure" inductors, i.e., they have zero resistance. If an inductor does have resistance then we can think of it as a pure inductor in series with a resistor.)

Consider the circuit (a) below.

When the switch is closed the current increases as shown on the right (b); i.e., it increases "gradually", at a rate determined by the values of L and R because of the "back-emf" induced in the inductor. It is instructive to look at the power dissipated in L and R, shown graphically below.

Note that if there was no inductor in the circuit then the power dissipated in the resistor (=i2R) would jump essentially instantaneously from zero to maximum when the switch was closed. However, with an inductor in the circuit, the power in the resistor rises more slowly to its maximum (asymtotic) value, because the current rises gradually, as shown in (b) above. So you can see that the inductor does have an effect on the power dissipated in the resistor; it causes the power to increase gradually. That can be desirable in devices in which a gradual increase in power to maximum is preferable.

Power is dissipated in the inductor also, as shown in (c). This is due to the "creation" of the magnetic field in the coil and that requires energy. The energy required is given by the area under the blue power curve, and it is stored as potential energy in the magnetic field/coil system.

In an a.c. circuit in which the inductor and resistor are in series, the inductor plays no role in the changing the power dissipated in the resistor. The reason is the average power dissipated in an inductor is zero; the power used to generate the magnetic field is returned to the circuit as the magnetic field collapses.

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