LC Resonance Calculator

An LC circuit oscillates at a natural resonant frequency where inductive and capacitive reactances are equal. This principle tunes radios, creates oscillators, and filters signals.

📻 Circuits📐 f = 1/2π√LC📻 Oscillators

Inductance L (μH)

Capacitance C (pF)

Please enter valid values.

Formula & Reference

Variable	Symbol	Formula	Units
Resonant Frequency	f	f = 1/(2π√LC)	Hz
Inductance	L	L = 1/(4π²f²C)	H
Capacitance	C	C = 1/(4π²f²L)	F
Angular Frequency	ω	ω = 1/√LC	rad/s
Impedance at Resonance	Z	Z = R (coil resistance)	Ω

Step-by-Step Examples

Example 1

AM Radio

L=100 uH, C=100 pF (variable to tune AM band).

f = 1/(2*pi*sqrt(100e-6*100e-12))
f = 1/(2*pi*sqrt(1e-14))
f = 1/(2*pi*1e-7) = 1.592 MHz

✓ 1.592 MHz — in AM broadcast band

Example 2

Tank Circuit

L=10 uH, C=1000 pF.

f = 1/(2*pi*sqrt(10e-6*1000e-12)) = 1.592 MHz

✓ 1.592 MHz — typical IF transformer tank

Example 3

FM Radio Tuner

Target 100 MHz with L=1 uH.

C = 1/(4*pi^2*f^2*L) = 1/(4*pi^2*(1e8)^2*1e-6)
C = 2.53 pF

✓ 2.53 pF needed for 100 MHz FM

Real-World Applications

📻

Radio Tuning

Variable capacitor adjusts C to select resonant frequency matching broadcast station.

⏰

Crystal Oscillators

LC principle extended to crystal oscillators for precise timing in microcontrollers.

📶

Wireless Power

Resonant coupling at matching LC frequency enables efficient wireless power transfer.

🔧

Band-pass Filters

LC tanks create sharp frequency selection in IF stages of superheterodyne receivers.

Common Mistakes to Avoid

⚠️

Using wrong units

Formula uses Farads and Henries. Convert: 100 uH = 100e-6 H, 100 pF = 100e-12 F.

⚠️

Ignoring parasitic elements

Real inductors have capacitance; real capacitors have inductance. Actual resonance may shift from ideal formula.

⚠️

Confusing series and parallel resonance

Series LC: minimum impedance at resonance. Parallel LC: maximum impedance at resonance. Different applications.

Frequently Asked Questions

What happens at resonance? ▾

Inductive reactance XL = 2*pi*f*L equals capacitive reactance XC = 1/(2*pi*f*C). Impedance is minimum (series) or maximum (parallel).

What is Q factor? ▾

Q = omega*L/R. Higher Q gives sharper resonance (narrower bandwidth). Quality of the tuned circuit.

How does radio tuning work? ▾

Variable capacitor changes C, shifting resonant frequency to match desired station. Circuit responds strongly to that frequency only.

What is bandwidth? ▾

BW = f_0/Q. Higher Q circuits have narrower bandwidth, selecting frequencies more precisely.

Can LC circuits sustain oscillation? ▾

Ideal LC oscillates forever. Real circuits lose energy to resistance. Amplifiers (oscillator circuits) replenish energy to maintain oscillation.

Related Physics Calculators

Formula Explorer connections

Interpretation: This relationship connects frequency, wavelength, speed, phase, intensity or resonance in an oscillating system. Assumption: Identify the medium, boundary conditions and reference frame. Linear waves, small amplitudes, nondispersive media or ideal resonance may be assumed.

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