# Extra Class question of the day: resonance

Yesterday, the National Committee of Volunteer Examiner Coordinators (NCVEC) question pool committee released the latest version of the Extra Class question pool, and I’m pleased to announce that I will be writing an Extra Class study guide. I’m planning on having it ready to release it at the Dayton Hamvention.

In conjunction with that, I’m also planning to do an “Extra Class Question of the Day” here on my blog. In reality, the “question of the day” will cover more than one question, as so many of them are related. As in my study guides, the correct answer will be highlighted, and the question will be marked with the pool question number.

Today’s question of the day is about resonance. Resonance is one of the coolest things in electronics. Resonant circuits are actually what makes radio, as we know it, possible.

What is resonance? Well, a circuit is said to be resonant when the inductive reactance and capacitive reactance are equal to one another. That is to say, when

2πfL = 1/2πfC

where L is the inductance in henries and C is the capacitance in farads.

For a given L and a given C, this happens at only one frequency:

f = 1/2π√(LC)

This frequency is called the resonant frequency. Resonance in an electrical circuit is the frequency at which the capacitive reactance equals the inductive reactance.(E5A02)

Let’s calculate a few resonant frequencies, using questions from the Extra question pool as examples:

The resonant frequency of a series RLC circuit if R is 22 ohms, L is 50 microhenrys and C is 40 picofarads is 3.56 MHz. (E5A14)

f = 1/2π√(LC) = 1/6.28x√(50×10-6 x 40×10-12) = 1/2.8×10-7 = 3.56 MHz

Notice that it really doesn’t matter what the value of the resistance is. The resonant frequency would be the same is R = 220 ? or 2.2 M?.

The resonant frequency of a series RLC circuit if R is 56 ohms, L is 40 microhenrys and C is 200 picofarads is 1.78 MHz. (E5A15)

f = 1/2π√(LC) = 1/6.28x√(40×10-6 x 200×10-12) = 1/5.6×10-7 = 1.78 MHz

The resonant frequency of a parallel RLC circuit if R is 33 ohms, L is 50 microhenrys and C is 10 picofarads is 7.12 MHz. (E5A16)

f = 1/2π√(LC) = 1/6.28x√(50×10-6 x 10×10-12) = 1/1.4×10-7 = 7.12 MHz

The resonant frequency of a parallel RLC circuit if R is 47 ohms, L is 25 microhenrys and C is 10 picofarads is 10.1 MHz. (E5A17)

f = 1/2π√(LC) = 1/6.28x√(25×10-6 x 10×10-12) = 1/9.9×10-7 = 10.1 MHz