ECE 1270: Introduction to Electric Circuits Lecture 18: Phasors Chapter 9: Sinusoidal Steady-State Analysis Section 9.3, 9.4

Representation of Complex Numbers Rectangular Form (real and imaginary) Imaginary Polar Form (magnitude and phase) Real Exponential Form

Phasors Phasor Transform or Phasor Representation 1) A phasor is a complex number that represents the amplitude and phase of a sinusoid 2) Phasors provide a simple means of analyzing linear circuits excited by sinusoidal sources

Phasors: Addition, Subtraction, Multiplication, and Division Amplitude and Phase Complex Conjugate Addition Subtraction Multiplication Division

Phasors Note that Vm is the amplitude and φ is the phase

Example 9.5: Hard Way Problem Solution  

Example 9.5: Easy Way Problem Solution Use Phasors

AP 9.1, AP 9.2

Phasor Notation for Resistor

Phasor Notation for Inductor +90° phase shift (voltage shifts to the left by 90 °) or Voltage leads Current by 90° in an Inductor How to verify in Multisim 1) Transient 2) AC Sweep

Phasor Notation for Capacitor -90° phase shift (voltage shifts to the right by 90 °) or Voltage lags Current by 90° in a Capacitor How to verify in Multisim 1) Transient 2) AC Sweep

Impedance and Reactance

AP 9.3, AP 9.4