8.4.2. COMBINATION OF L AND C, RESONANT (TUNED) CIRCUITS

Combinations of inductors and capacitors have always a special characteristic referring to their RESPONSE to different frequencies. If we want to understand their behaviour we have two main possibilities:

FREE OSCILLATING CIRCUIT

Let us suppose a capacitor is charged with a certain voltage. As soon as this capacitor is connected across an inductor there starts to flow a current. The amount of current is slowly increasing because of the self-induced voltage across the coil.

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On the one hand this current is discharging the capacitor which lets drop the voltage of the capacitor. On the other hand the increasing current is building up a magnetic field around the coil. The current will reach its maximum just when the capacitor is discharged totally. At that very instant the voltage at the capacitor is Cero while the current is at its maximum, and therefore the magnetic field has its maximum too.

figure

There is no charge left at the capacitor, therefore the capacitor cannot deliver any current anymore. Combinations of inductors and capacitors have always a special characteristic referring to their RESPONSE to different frequencies. If we want to explain their behaviour we have two main possibilities:

FREE OSCILLATING CIRCUIT

Let us suppose a capacitor is charged with a certain voltage.

As soon as this capacitor is connected across an inductor there starts to flow a current. The amount of current is slowly increasing, because of the selfinduced voltage across the coil.

On the one hand this current is discharging the capacitor which lets drop the voltage of the capacitor. On the other hand the increasing current is building up a magnetic field around the coil.

The current will reach its maximum just when the capacitor is discharged totallyted across an inductor.

At that very instant the voltage at the capacitor is Cero while the current is at its maximum, and therefore the magnetic field has its maximum too.

There is no charge left at the capacitor, therefore the capacitor cannot deliver any current anymore. The current will have to vanish, but it will not stop to flow immediately. As soon as the current will be Cero the magnetic field must have vanished too. But before this can be the case, the magnetic field has to collapse first. The collapsing field will induce a voltage across the coil which will have a direction opposite to the voltage connected to it when the current started to flow.

This selfinduced voltage will cause a current to flow. This current will have the same direction as before, and it will charge the capacitor again but now in opposite direction.

As soon as the magnetic field has vanished totally the capacitor will be charged again to a voltage of the same amount as it was in the beginning, but in opposite direction.

Now the same process will start again, and cause a second halfwave of a sinusoidal ac-current and voltage. Summarizing: If we inject some electric energy to a parallel connection of a capacitor and an inductor there will appear an ac-voltage across the circuit with a frequency depending on the inductance and on the capacity.

But in reality these oscillations will fade out very soon, because the current flowing in this circuit to and for has to pass some obstacles. So for example the resistance of the wires forming the coil, or the resistance of the interconnecting wires. There will vanish also some of the charges stored in the capacitor by moving through the insulating dieelectricum.

All in all, after a short time we will find no more oscillations.

We can explain this effect also from another point of view:

ENERGY CONSIDERATIONS

If we look at the process explained in the last chapter from the point of view of energy, we will find that this LC combination is behaving very similar like a pendulum.

fig. 77

fig. 78

A pendulum starts with a lifted mass which means there is POTENTIAL MECHANICAL ENERGY

When released, the mass gains more and more velocity during its movement downward to the lowest point. In terms of energy: the potential energy is turned into CINETIC ENERGY.

This cinetic energy will cause the mass moving on upwards after passing the lowest point and - by moving upward again - turning the cinetic energy back into POTENTIAL MECHANICAL ENERGY.

TUNED CIRCUIT

Starts with seperated charges on the plates of the capacitor which means ELECTRIC ENERGY.

Once connected to the inductor, the capacitor starts to discharge and push current through the inductor. The current will cause a magnetic field in the inductor and - as soon as the capacitor is totally discharged - the former electric energy is turned into MAGNETIC ENERGY.

So the capacitor is free of charges now, it cannot supply any current anymore, and therefore the magnetic field starts to collapse now.

The collapsing magnetic field induces a voltage and causes the current to go on flowing as before.

This will charge the capacitor no in opposite direction as before. This effect goes on till the capacitor is charged again and the magnetic field has been turned into ELECTRIC ENERGY again.

CHECK YOURSELF:

1. Describe the construction of a tuned circuit.
2. Describe what happens in such a circuit after some energy into it.
3. Explain the similarities between pendulum and resonant circuit.
4. What is the reason for the fast vanishing of oscillations in such a circuit?