- [Instructor] If you connect a charged capacitor across an inductor, you will see a beautiful energy exchange take place between the two elements. These energy oscillations, look as if the capacitor is saying, you take the energy, and the inductor then says, no you take my energy. Why don't any of these elements store the energy and become settled?
Let's have a look at the interesting physics behind these oscillations, and some of the applications. Before diving into the LC circuit, we need to understand a simple circuit. A capacitor resistor circuit.
The capacitor is fully charged initially. Let's introduce a resistor into the circuit. Here you can observe that initially the current flow is at the maximum, and then it sharply decays with time.
This is expected, because at the beginning, the charge difference is at the maximum, so the current has to be at the maximum. No let's see what will happen if the resistor is replaced with an inductor. Here again, the capacitor is fully charged initially.
It's quite logical to expect that there will be a huge current flow at the beginning. And then the current flow would reduce, as in the previous case. However, this will not happen in practice.
An inductor develops EMF across it, based on the change in current flow. This means that a drastic change in current is not possible across the inductor, as in the previous case. Now the current flow starts from zero and increases to the maximum, and then comes back to zero again.
In an inductor capacitor circuit, the current flow variation has to be gradual, and here we can see that the current flow in the LC circuit, is shaped like a sign curve. Let's look at the electron flow animation once again. The current in the circuit, starts from zero, and gradually achieves the maximum value.
In the next one quarter of a time period, the current from the capacitor, starts to decrease, resulting in another change in current. At the end of the capacitor discharge, if you check the EMF across the inductor, it will have the opposite polarity to the initial EMF. This reverse EMF charges the capacitor with the opposite polarity.
In the next half of the time period, the capacitor will be fully charged with the reverse polarity. This also means that the current flow will be in the reverse direction for the next half. Hence, in an ideal circuit, this back and forth flow of current, would continue to charge and discharge the capacitor and form endless oscillations of energy.
However, practically we can never achieve such ideal behavior, due to the presence of resistance. The resistance causes energy decay in the form of heat. This means that in a practical circuit, the oscillations will die out eventually.
As we increase the resistance, the oscillations die out very quickly, as shown. If we increase the resistance further, to some critical value, there would be no oscillation at all. Underdamped LC circuits have many applications in industry, namely, thyristors, magnetrons, et cetera.
In communication systems they are an integral part of frequency filters. Please don't forget to support us. Thank you.
