LCR Circuit Resonance Calculator Physics

f0 = ---
Z = ---
φ = ---
100
10.0
1.00
5.00
f0: -- XL: -- XC: -- Z: -- Power Factor: --

What is the LCR Circuit Resonance Calculator?

Quick Answer: An interactive tool that computes impedance, reactances, resonant frequency, and power factor for a series LCR circuit. Adjust R, L, C, and frequency to see the resonance curve and how Z and phase change near the resonant point. Perfect for JEE, NEET, and physics lab.

Theory of Series LCR Resonance

In a series LCR circuit, the impedance is Z = √(R² + (XL - XC)²), where inductive reactance XL = 2πf L and capacitive reactance XC = 1/(2πf C). The phase angle φ = tan−1((XL - XC)/R). Resonance occurs when XL = XC, giving f0 = 1/(2π√(LC)). At resonance, impedance is minimum (Z = R) and power factor is unity (cosφ = 1). The graph plots Z vs. frequency, showing a sharp dip at f0.

Step-by-Step Examples

Example 1: Finding Resonant Frequency

  1. Set R=100 Ω, L=10 mH, C=1 μF. Click "Go to Resonance". The frequency slider jumps to f0 = 1/(2π√(0.01×1e-6)) = 1.59 kHz.
  2. At resonance, Z = R = 100 Ω, power factor = 1. The graph shows the minimum point.

Example 2: Off-Resonance Behaviour

  1. Move frequency to 5 kHz. XL becomes larger than XC, Z increases, power factor drops below 1.
  2. Phase angle becomes positive (inductive).

Example 3: Effect of Resistance

  1. Change R to 50 Ω. The resonance dip becomes sharper (higher quality factor Q). Impedance at resonance is 50 Ω.

Frequently Asked Questions

What is resonant frequency?

The frequency at which inductive and capacitive reactances cancel, making the circuit purely resistive with minimum impedance. Given by f0 = 1/(2π√(LC)).

Why does impedance drop to R at resonance?

Because XL = XC, so their difference is zero. Only resistance R remains, making Z = R.

How does power factor change with frequency?

It is cosφ = R/Z. At resonance, Z=R so power factor=1. Away from resonance, Z increases, power factor decreases.

What is the significance of the resonance curve?

The Z vs. f graph shows the sharpness of resonance. A narrower dip indicates high Q factor (low R), used in tuning circuits.

Can I calculate Q factor?

Q = ω0L / R = 1/(ω0C R). The tool shows f0 and bandwidth; you can compute Q manually if needed.