Resonant Frequency
With inductance 10 mH, capacitance 100 nF, frequency you want instead 7000 Hz, resonant frequency comes to 5,032.92 Hz — resonant frequency. It is reached in 5 steps, the last of which is 1 / (2 * pi * sqrt(0.01 * 0.0000001)), and each one is printed on the page with its numbers filled in. The formula is the one published by NIST Special Publication 811, not an approximation fitted to it.
Resonant frequency of an LC circuit from inductance and capacitance, with the angular frequency, the period and the capacitance a target frequency needs.
Formula and sources checked · How we check
Inductance 10 mH, Capacitance 100 nF, Frequency you want instead 7000 Hz
5,032.92 Hz
Resonant frequency for the example below. Editing a field recomputes the calculator below; this figure holds the answer the page was loaded with.
It is written into the HTML rather than drawn by a script, so a search engine reading this page without running JavaScript still finds an answer.
- Resonant frequency
1 / (2 * pi * sqrt(0.01 * 0.0000001))5,032.921 Hz- In kilohertz
5032.9212 / 10005.033 kHz- Angular frequency ω
2 * pi * 5032.921231,622.777 rad/s- Period
1 / 5032.92120 s- Capacitance for the target frequency
1000000000 / (0.01 * (2 * pi * 7000) ^ 2)51.694 nF
Worked example
10 mH with 100 nF resonates at 5,032.92 Hz — a period of 0.0001987 seconds. To move it to 7 kHz on the same coil the capacitance has to drop to 51.69 nF, because the frequency goes as the inverse square root: halving the capacitance raises the frequency by a factor of √2, not 2.
How to work it out yourself
- 1.Watch the prefixes. Millihenries and nanofarads are what components are actually marked in, and this form converts them; entering henries and farads directly gives an answer off by a factor of a million.
- 2.The frequency depends on the product LC, so any pair with the same product resonates at the same place. Which pair you pick changes the impedance and the current, not the frequency.
- 3.To retune, change the capacitor. Variable capacitors exist, adjustable inductors are awkward, and the last line gives the capacitance a target frequency needs on the coil you already have.
The formula
- Resonant frequency
1 / (2 * pi * sqrt(0.01 * 0.0000001)) - In kilohertz
5032.9212 / 1000 - Angular frequency ω
2 * pi * 5032.9212 - Period
1 / 5032.9212 - Capacitance for the target frequency
1000000000 / (0.01 * (2 * pi * 7000) ^ 2)
Source: NIST Special Publication 811 — guide for the use of the SI, BIPM — the SI Brochure, the henry and the farad
Questions people actually ask
- Why is the frequency an inverse square root?
- Energy sloshes between the coil’s magnetic field and the capacitor’s electric field, and the round trip takes 2π√(LC). Both components store more energy as they grow, so both slow the oscillation, and each contributes only its square root.
- Does resistance change the resonant frequency?
- Barely, in a practical circuit. Resistance damps the oscillation and broadens the peak — that is the Q factor — but the centre frequency shifts only when the damping is heavy. For most tank circuits the LC formula is the whole answer.
- What is the difference between series and parallel resonance?
- The frequency formula is the same. What differs is the impedance: a series LC drops to almost nothing at resonance and a parallel LC rises to almost everything, which is why one is used to pass a frequency and the other to block it.
Related
- LED Resistor CalculatorThe series resistor an LED needs, from supply voltage, forward voltage and current — with the power it must dissipate and which standard value to pick.
- Parallel ResistorsUp to four resistors in parallel or series, with the current each one takes and the power it has to dissipate — which is what decides the rating.
- Ohm's Law CalculatorVoltage, current, resistance and power from any two of them, with the whole set printed rather than the one you asked for.
- Resistor Colour Code CalculatorResistance and tolerance from the bands on a resistor, with the E-series value it is meant to be.
- Voltage Drop CalculatorVoltage lost along a copper or aluminium run, as volts and as a percentage, against the 3% the NEC recommends for a branch circuit.
- Watts to AmpsWatts to amps and back, with the power factor and the phase that AC needs. A DC answer applied to a 3-phase motor is out by 73%.
Put this calculator on your site
Free, no attribution required beyond the link.
<iframe src="https://rulecalculators.com/embed/resonant-frequency" width="100%" height="420" style="border:1px solid #e7e4de;border-radius:12px" title="Resonant Frequency"></iframe>