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The Coil and Electric Energy :



In the first place, we must know whether the coil is a dissipative element of electrical energy in the same way as the resistance or, conversely, a conservative element of electric energy like the capacitor.

To facilitate our task, we must consider the phenomenon of mutual inductance which, let us recall, occurs between two distinct circuits.

Figure 11 shows an inductive circuit and an induced circuit.


The induced current I2 appearing in the turn of the induced circuit passes through the resistor inserted in this circuit : it thus dissipates a power determined by the product of the resistor R by the square of the current (I22).

This power can not however have been directly produced by the induced circuit since we do not note the presence of any generator in it. The only generator present is the battery of the inductive circuit, or this battery is not connected to the induced circuit. The transfer of energy between the two circuits is therefore carried out by the induction flux that the two turns put in common.

We must then admit that the electric power supplied by the battery to the inductor circuit is not totally dissipated in it but also produces an induction flux which is in turn converted back into electrical power dissipated in the induced circuit. We can conclude that the coil is a conservative element of energy like the capacitor since it does not dissipate this energy entirely.

To have a closer analogy with the capacitor, we can say: as the capacitor stores electrical energy by creating an electric field between its armatures, the coil stores the electrical energy by creating a magnetic field around its turns. Unlike the capacitor to which a voltage must be applied between its armatures to create an electric field, it is necessary to circulate a current in a coil so that it generates a magnetic field.

We know that the energy Wc stored in a capacitor depends on the square of the voltage applied between its plates and the capacity of the capacitor, that is :

Wc = (1 / 2) x CV2

In the same way, the energy stored by a coil depends on the square of the current which crosses it multiplied by the inductance of this coil, all divided by 2, namely :

WL = (1 / 2) x LI2

WL : Electric energy stored in J.

L : Inductance in H

I : Intensity in A

In a similar way to what has been said for the capacitor, the coil stores only half of the energy supplied by the generator. The second half is dissipated in the resistance equivalent to the circuit including the internal resistance of the generator.

Note however that in the case of the capacitor, the generator provides a current only during the charging of the capacitor, because once it loaded, all current flow ceases, as well as any dissipation of energy to which it gives rise. In the case of the coil, the current must flow continuously since it is precisely he who creates the magnetic field in the coil by its variations. The accompanying energy consumption therefore also persists.

We deduce from these observations that the coil consumes more energy than the capacitor to store the same amount.

The coil finds its use in the circuits traversed by currents of variable intensity.

In the next lesson, we will analyze this type of current, one of whose forms is particularly familiar to you since it is about alternating current.