### Prerna Gupta

A post graduate in Control and Instrumentation. Currently she is product manager at Lesics engineers Pvt.Ltd. Her areas of interest are Telecommunication, Semiconductor Material and devices, Embedded systems and design. Prerna has done projects such as MOSFET, Optical fiber cable, Routing, GPS System, Modulation, Satellite, Working of Mobile phone, Electromagnetic radiation Etc.

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# The Interesting Physics Behind LC Oscillations

I connect a charged capacitor across an inductor, a beautiful energy exchange or oscillation takes place between the two elements. Let’s have a look at the interesting physics behind these oscillations, and some of the applications.

## How does a simple capacitor-resistor (RC) circuit work?

Before diving into the LC circuit, I will explain a simple circuit; capacitor-resistor circuit (Fig.1A). The capacitor is fully charged initially, let’s introduce a resistor into the circuit. Here we can say that initially the current flow will be at maximum and then it sharply decays with time (Fig.1B) . This is expected because at the beginning, the charge difference is at maximum, so the current has to be at maximum.

## How does an inductor-capacitor (LC) circuit work?

Now I will explain 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 will reduce as in the RC circuit. However, this will not happen in practice. Based on the change in current flow an inductor develops EMF across it. This means that a drastic change in current is not possible across the inductor. 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 the current flow in the LC circuit is shaped like a sine curve. The current in the circuit starts from zero and gradually achieves the maximum value (Fig.3A) and in the next one quarter of a time period, the current from the capacitor starts to decrease, resulting in another change in current (Fig.3B).

At the end of the capacitor discharge, if I 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 (Fig.4A). 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 (Fig.4B).

However, practically, we can never achieve such ideal behaviour due to the presence of resistance. This resistance causes energy decay in the form of heat. It 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 in Fig.5. Further on if I increase the resistance to some critical value, there would be no oscillation at all.

## Applications of LC circuits

1. The underdamped LC circuits have many applications in Industry, namely Thyristors, Magnetrons,... etc.

2. In Communication systems, they are an integral part of frequency filters.