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Current and frequency in series RLC

Short answer

Current is minimum at low and high frequencies, peaking at resonant frequency f₀ where X_L=X_C, impedance Z=R (minimum). Below f₀ circuit capacitive, current leads; above, inductive, current lags. The bell-shaped curve’s sharpness depends on R.

Describe briefly: Current and supply frequency relationship of a RLC series circuit

In a series RLC circuit the impedance is

Z = √(R² + (ωL − 1/ωC)²), and the current is I = V/Z.

Because X_L = ωL rises with frequency and X_C = 1/(ωC) falls with it, the current changes with frequency as follows.

  • Low frequency (f < f₀): X_C is large and X_C > X_L. The circuit is capacitive, Z is large and the current is small. The current leads the voltage.

  • At resonance (f = f₀): X_L = X_C, so they cancel. Z = R (minimum) and the current is maximum, I₀ = V/R, in phase with the voltage (unity power factor).

    f₀ = 1/(2π√(LC))

  • High frequency (f > f₀): X_L > X_C. The circuit is inductive, Z increases and the current falls. The current lags the voltage.

   I
   │              I0 = V/R
   │               _.-._
   │             /       \
   │            /         \
   │          /             \
   │  ___..-'                 '-..___
   └────────────────┴───────────────────── f
                    f0

The curve is bell-shaped (a resonance curve). A small R gives a tall, narrow (sharp) peak and a high quality factor Q = ω₀L/R. A large R gives a flatter, wider peak. The bandwidth is BW = f₂ − f₁ = f₀/Q, measured between the half-power points where I = I₀/√2.

✓ Answer checked by Claude Opus 5.5 (high effort)

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