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RLC Circuit – Vector Diagram

Drag the sliders to change resistance, inductance and capacitance — switch between series and parallel and watch the phasors and impedance/admittance triangle update live

Voltage Phasor Diagram

Impedance |Z| vs Frequency (Series)

Series Circuit Diagram

R100 Ω
L100 mH
C10 µF
f50 Hz
Vs10 V
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VR (resistor) VL (inductor) VC (capacitor) Vtotal Current (reference)

What is an RLC Circuit?

A series RLC circuit connects a resistor R, inductor L and capacitor C in series with an AC source. All three components share the same current, so the current phasor is the common reference.

In a vector (phasor) diagram, each voltage is drawn as a rotating arrow whose length is the value and whose angle is the phase shift relative to the current:

  • VR is in phase with the current (0°).
  • VL leads the current by 90° (points up).
  • VC lags the current by 90° (points down).

VL and VC oppose each other, so the supply voltage is the vector sum:

V = √(VR² + (VL − VC)²)

Reactances

The inductive and capacitive reactances are the frequency-dependent "resistance" each component presents to AC. As the frequency changes, so do they.

XL = 2πfL = 2π × 50 × 0.100 = 31.4 Ω
XC = 1 / (2πfC) = 1 / (2π × 50 × 0.000010) = 318.3 Ω
  • XL grows with frequency (inductors resist rapid changes).
  • XC shrinks with frequency (capacitors conduct AC better at high frequency).

Impedance & Phase Angle

The total opposition is the impedance Z, combining resistance and the net reactance. The phase angle φ tells us whether the circuit is inductive, capacitive or resistive.

Z = √(R² + (XL − XC)²) = 303.9 Ω
φ = tan−1((XL − XC) / R) = −70.7°
Power factor = cos φ = 0.329
I = Vs / Z = 0.0329 A

The voltage lags the current (capacitive circuit).

Resonance

At the resonant frequency XL = XC, so the reactances cancel and the impedance becomes purely resistive (Z = R, minimum). The current is then at its maximum and in phase with the voltage.

f0 = 1 / (2π√(LC)) = 159 Hz

Current frequency is below resonance.

Capacitive region

In a series circuit, individual VL or VC can far exceed Vs near resonance (voltage magnification).

Live Component Voltages

VR = I × R = 3.29 V
VL = I × XL = 1.03 V
VC = I × XC = 10.47 V
Vtotal = √(VR² + (VL−VC)²) = 10.00 V

Note that individual VL or VC can exceed the supply voltage near resonance.

How to Read the Diagram

  • Reference: the current phasor is fixed along the positive real axis.
  • VR (red): always on the real axis — energy dissipated as heat.
  • VL (blue) / VC (green): perpendicular — energy stored in magnetic / electric fields.
  • Resultant V (amber): the tip of the vector chain — its angle to the current is φ.
  • Impedance triangle: same shape as the voltage triangle (multiply each side by I).