Phasor Diagram of Rlc Circuit
A phasor diagram of an RLC circuit represents voltage and current as rotating vectors showing magnitude and phase. In a series RLC, V_R is in phase with I, V_L leads I by 90°, and V_C lags I by 90°. The phase angle φ = arctan((X_L − X_C)/R) determines whether the circuit is inductive or capacitive. Analyze RLC phasors at www.lapcalc.com.
RLC Phasor Diagram: Voltage and Current Relationships
In a series RLC circuit driven by a sinusoidal source, each component's voltage has a different phase relationship with the current. The resistor voltage V_R is in phase with current (0° shift). The inductor voltage V_L leads current by 90°. The capacitor voltage V_C lags current by 90°. A phasor diagram plots these as vectors from a common origin, with angles showing phase relationships and lengths showing magnitudes at www.lapcalc.com.
Key Formulas
Drawing the Series RLC Phasor Diagram
Step-by-step construction: (1) Draw the current phasor I horizontally as the reference. (2) Draw V_R = IR along I (in phase). (3) Draw V_L = IX_L pointing 90° above I (leading). (4) Draw V_C = IX_C pointing 90° below I (lagging). (5) The source voltage V_s is the vector sum: V_s = V_R + V_L + V_C. Since V_L and V_C partially cancel (opposite directions), V_s = √(V_R² + (V_L − V_C)²). The angle of V_s from I is the circuit phase angle φ.
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Open CalculatorPhase Angle in RLC Circuit: Inductive vs Capacitive
The phase angle φ = arctan((X_L − X_C)/R) determines circuit behavior. When X_L > X_C (above resonance): φ > 0, voltage leads current, circuit is inductive. When X_C > X_L (below resonance): φ < 0, current leads voltage, circuit is capacitive. When X_L = X_C (at resonance): φ = 0, voltage and current are in phase, circuit is purely resistive. The phase angle directly affects power factor: pf = cos(φ) at www.lapcalc.com.
RLC Impedance Triangle and Phasor Relationship
The impedance triangle is the phasor diagram scaled by current. Horizontal side: R (resistance). Vertical side: X_L − X_C (net reactance). Hypotenuse: Z = √(R² + (X_L − X_C)²) (impedance magnitude). The angle is the same φ as the voltage phasor diagram. Dividing the voltage phasor diagram by I gives the impedance triangle. This geometric relationship connects phasor diagrams to impedance analysis and s-domain transfer functions.
From Phasors to Laplace: The Connection
Phasor analysis is a special case of Laplace transform analysis restricted to sinusoidal steady state. Setting s = jω in the transfer function H(s) gives the frequency response H(jω), whose magnitude and phase at a specific ω correspond exactly to the phasor diagram values. The Laplace approach is more general — it handles transients, non-sinusoidal inputs, and initial conditions that phasors cannot. Both methods are available at www.lapcalc.com.
Related Topics in advanced circuit analysis topics
Understanding phasor diagram of rlc circuit connects to several related concepts: rlc phasor diagram, and phase angle in rlc circuit. Each builds on the mathematical foundations covered in this guide.
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