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RC Circuit Phasor Diagrams

Sep 30, 2025

Overview

This lecture explains voltage and impedance phasor diagrams for AC RC circuits, covering voltage relationships, phase angles, and calculation methods for source voltage, current, and impedance.

RC Circuit Basics

  • An RC circuit has a resistor, a capacitor, and an AC voltage source.
  • In a purely resistive circuit, voltage and current are in phase (phase angle = 0°).
  • In a purely capacitive circuit, current leads voltage by 90°.

Phasor Diagrams for Voltage

  • The current vector is drawn along the positive x-axis.
  • Voltage across a resistor (VR) is in phase with current (along x-axis).
  • Voltage across a capacitor (VC) lags current by 90° (drawn along negative y-axis).
  • The total source voltage (VS) is the vector sum of VR and VC.
  • The phasor diagram forms a right triangle, with VS as the hypotenuse.

Voltage and Current Calculations

  • Ohm’s law for resistor: VR = I × R.
  • Capacitive reactance for capacitor: VC = I × XC, with XC being the capacitive reactance.
  • Source voltage: VS = √(VR² + VC²).
  • Current: I = VS / √(R² + XC²).
  • Use RMS or peak values consistently for voltage and current.

Phase Angle in RC Circuits

  • Phase angle (φ) indicates how much current leads voltage in RC circuits.
  • Phase angle: tan(φ) = VC / VR = XC / R.
  • φ is between 0° (pure resistor) and 90° (pure capacitor).

Impedance in RC Circuits

  • Impedance (Z) is the total opposition to AC current, combining resistance and reactance.
  • Resistance is drawn along the positive x-axis, reactance along negative y-axis in the impedance phasor diagram.
  • Total impedance: Z = √(R² + XC²).
  • The phase angle from the impedance triangle matches that from the voltage triangle.

Key Terms & Definitions

  • Phasor diagram — A graphical way to show the relationships between AC voltages/currents as vectors.
  • Capacitive reactance (XC) — Opposition to AC current by a capacitor; XC = 1/(ωC).
  • Impedance (Z) — Total opposition to AC current in a circuit, combining resistance and reactance.
  • Phase angle (φ) — The angular difference by which current leads or lags voltage.
  • RMS (root mean square) — A method of expressing AC voltages/currents as equivalent DC values.

Action Items / Next Steps

  • Review calculation examples for RC circuits in upcoming videos.
  • Practice drawing voltage and impedance phasor diagrams.
  • Ensure correct use of RMS vs. peak values in calculations.

Full transcript