Lecture 11 EEE 302 Electrical Networks II Dr. Keith E. Holbert Summer 2001

Lecture 12 Electrical Analogies (Physical)

Lecture 13 Phasors A phasor is a complex number that represents the magnitude and phase of a sinusoidal voltage or current:

Lecture 14 Class Examples Extension Exercise 8.3 Extension Exercise 8.4

Lecture 15 Complex Numbers x is the real part y is the imaginary part z is the magnitude  is the phase  z x y real axis imaginary axis Polar: z   = A = x + jy :  Rectangular

Lecture 16 Complex Number Addition and Subtraction Addition is most easily performed in rectangular coordinates: A = x + jyB = z + jw A + B = (x + z) + j(y + w) Subtraction is also most easily performed in rectangular coordinates: A - B = (x - z) + j(y - w)

Lecture 17 Complex Number Multiplication and Division Multiplication is most easily performed in polar coordinates: A = A M   B = B M   A  B = (A M  B M )  (  ) Division is also most easily performed in polar coordinates: A / B = (A M / B M )  (  )

Lecture 18 Circuit Element Phasor Relations (ELI and ICE man)

Lecture 19 Class Examples Extension Exercise 8.5 Extension Exercise 8.6 Extension Exercise 8.7

Lecture 110 Impedance AC steady-state analysis using phasors allows us to express the relationship between current and voltage using a formula that looks likes Ohm’s law: V = I Z Z is called impedance (units of ohms,  ) Impedance is (often) a complex number, but is not a phasor Impedance depends on frequency 

Lecture 111 Impedance Summary

Lecture 112 Z eq Series Impedance Z1Z1 Z eq = Z 1 + Z 2 + Z 3 Z3Z3 Z2Z2

Lecture 113 Parallel Impedance 1/Z eq = 1/Z 1 + 1/Z 2 + 1/Z 3 Z3Z3 Z1Z1 Z2Z2 Z eq

Lecture 114 Class Examples Extension Exercise E8.10 Extension Exercise E8.8