How to Calculate Frequency in an LC Tuned Circuit

Have you ever wondered how frequency in an LC tuned circuit is determined? You’re not alone—this is a key concept that every aspiring electronics engineer should grasp, especially when preparing for challenging exams. So, let’s roll up our sleeves and get into it!

First things first, what exactly is an LC tuned circuit? Simply put, it’s a circuit consisting of an inductor (L) and a capacitor (C) that oscillates at a certain frequency. This oscillation is due to the energy exchange between the magnetic field of the inductor and the electric field of the capacitor. Cool, right?

Now, the frequency of these oscillations can be calculated using a simple formula:

[ f = \frac{1}{2\pi\sqrt{LC}} ]

Where:

• ( f ) is the frequency in hertz (Hz)
• ( L ) is the inductance in henries (H)
• ( C ) is the capacitance in farads (F)

I can almost hear the wheels turning in your mind—let's break this down with some numbers to bring it all to life.

Let’s take an example. Suppose we have:

• ( L_1 = 58.6 , \mu H )
• ( C_1 = 300 , pF )

Before we jump into calculations, we need to convert these units into henries and farads:

• ( L = 58.6 \times 10^{-6} , H )
• ( C = 300 \times 10^{-12} , F )

With our units all set, it’s time to plug these values into our formula. When calculating ( L \times C ), we find:

[ L \times C = 58.6 \times 10^{-6} \times 300 \times 10^{-12} = 1.758\times 10^{-16} ]

This is key because we need it under the square root of the formula. Remember, it’s like setting up a perfect recipe: the ingredients need to be ready first!

Now comes the fun part—substituting back into our formula:

[ f = \frac{1}{2\pi\sqrt{1.758 \times 10^{-16}}} ]

Crunching those numbers gives us the frequency of oscillations, and voila! you find out the answer is approximately 1199 kHz.

So out of the options, the correct choice is B: 1199 kHz. It might seem like a lot of math, but don’t worry—you’ll get the hang of it with practice!

Let’s pause and reflect for a moment. Why is this concept so vital? Understanding oscillations helps improve everything from radio reception to even the basic functions of mobile phones. In a world so driven by technology, grasping these fundamentals isn’t just about passing an exam; it’s about becoming part of a broader story in electronics engineering.

In closing, make sure you practice these calculations. Tackle similar problems, and don’t hesitate to loop back and review the formulas. Each time you do, those numbers and concepts will stick a little more.

Ready to tackle that ELEX exam? With the right knowledge under your belt, you’re well on your way!