LC Circuit Resonant Frequency Calculator
Calculate the resonant frequency of an LC circuit from inductance and capacitance.
Shows frequency in Hz, kHz, and angular frequency in rad/s.
An LC circuit (also called a tank circuit or resonant circuit) consists of an inductor L and capacitor C connected together. It oscillates at a specific natural frequency:
f₀ = 1 / (2π√(LC)) ω₀ = 1 / √(LC) (in radians per second)
At resonance:
- The inductive reactance equals the capacitive reactance: XL = XC
- Energy oscillates between the magnetic field (inductor) and electric field (capacitor)
- In an ideal LC circuit (no resistance), oscillations continue forever
Real-world applications:
LC circuits are the heart of:
- Radio tuning — AM radio uses variable capacitors to select stations (typical range: 550–1600 kHz)
- Crystal oscillators — quartz crystals behave as high-Q LC circuits for precise frequency references
- Wireless charging — transmitter and receiver LC circuits resonate at the same frequency (typically 6.78 MHz or 13.56 MHz)
- Switch-mode power supplies — LC filters smooth the output voltage
Quality factor Q: Real LC circuits have some resistance R, giving Q = (1/R)√(L/C). High Q means sharper resonance and better frequency selectivity.
Intuition: At frequencies below resonance, the capacitor dominates (high impedance). Above resonance, the inductor dominates. At resonance, the two cancel and impedance is minimum (series) or maximum (parallel).