Transpose Resonant Frequency Formula

Transposing the resonance formula to find L or C is something all GCSE students should be able to do. You might get a question where they give you the resonance frequency and you have to calculate the capacitance (C) or the inductance (L) of the coil. In this case, an online calculator will not help you! It is better to learn to transpose the formula so you can find the unknown quantity. However, if you need to check your answers, then you can always use my parallel tuned circuit calculators on this site.

I like to bring all the terms in the denominator to the LHS.

We now divide throughout by the terms we do not need, which brings them on the RHS.

We now square both sides to eliminate the square root on the LHS to give the term for LC.

Formula for Inductance L

Formula for Capacitance C

I can simplify this further to make it look nice algebraically, however bearing in mind that you will be using a calculator, it is better to leave it like this to reduce the tapping overhead. This way you work out the contents inside the brackets and then hit the square button on the calculator only once. If you were using a calculator, it is common to start with the following sequence.

1. Multiply the following, 2 × π × f
2. Then hit the reciprocal button
3. Then hit the square button
4. Finally, divide by the value of L

Ideally, you want to avoid having to write long numbers, and tapping them back into the calculator, because that is where students usually make mistakes.

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