Question

What is the frequency of an LC oscillator?

Answer 1

In the question, we are asked to define the frequency of an LC oscillator. One could begin by explaining what an LC circuit is and also mention the use of LC oscillators. Now you could move on to explaining the significance of an LC oscillator as an answer to the above question.

Complete answer:
Before going into the discussion on the frequency of an LC circuit we have to understand what exactly is an LC circuit and what its significance is.
LC circuits are circuits that generate signals of a particular frequency or maybe select a particular signal from a complex signal. LC circuits basically comprises two main components: the inductor (L) and the capacitor (C) and they can either be connected in series or in parallel with each other.
LC oscillator’s application lies in the generation of high frequency waves. There exists a certain combination of values for L and C in which the circuit is said to be tuned or in resonance. Here the inductive and capacitive reactance are known to be identical and hence cancel each other. So, at resonance we have,
${{X}_{L}}={{X}_{C}}$
$\Rightarrow 2\pi fL=\dfrac{1}{2\pi fC}$
$\therefore f=\dfrac{1}{2\pi \sqrt{LC}}$
Here, f is the resonant frequency in units of hertz (Hz), L is the inductance in Henries (H) and C is the capacitance in units of Farads.

Note: One could see that inductive and capacitive reactance are directly and indirectly proportional to the frequency respectively. For the same reason, at lower frequencies, the inductor behaves as a short circuit and the capacitor acts as an open circuit. The reverse of this happens at higher frequencies.