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CIRCUITS & RESONANCE

Resonant frequency (LC circuit) calculator

Choose what you want to find: the frequency, the coil, or the capacitor. Enter the other two values and the answer appears.

  1. 1Type your numbersUse the white boxes. Tap an example chip if you want a starting point.
  2. 2Read the answerThe green panel updates as you type. You cannot edit it.
  3. 3See whyThe steps below show the formula with your numbers filled in.
TRY AN EXAMPLE
YOUR NUMBERS · TYPE IN THE WHITE BOXES
WHAT DO YOU WANT TO FIND?
Calculated
MHz
Worked out from the other two.
µH
 
pF
 
THE ANSWER · WORKED OUT FOR YOU
Resonant frequency
5.033MHz

Bigger coil or capacitor, lower frequency. Smaller, higher.

HOW IT WAS WORKED OUT
f = 1 ÷ (2π × √(L × C))
f = 1 ÷ (2π × √(10 µH × 100 pF)) = 5.033 MHz

What this means

A coil (inductor) and a capacitor swap energy back and forth. At one frequency they do it most easily. That is the resonant frequency, and it is how radios pick one station out of many.

Make the coil or the capacitor bigger and the resonant frequency drops. Make either smaller and it rises.

fᵣ = 1 / (2π √(L × C))
ON THE EXAM

Units trip people up. Inductance here is in microhenries and capacitance in picofarads, which gives the answer in megahertz.

42 questions in the official pools involve this topic:

Common questions

Why microhenries and picofarads?

They are the sizes used in radio circuits, and they combine so that the answer comes out directly in megahertz. The calculator converts to base units for you.

What if I know the frequency and one part?

Switch the 'Find' control to Inductance or Capacitance, enter the frequency and the part you know, and it solves for the other.

Is this the same for a trap or filter?

Yes. A trap, a tuned filter and a tank circuit all use the same resonance formula.

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