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EEE 302 Electrical Networks II Dr. Keith E. Holbert Summer 2001 Lecture 1 1 Electrical Analogies (Physical) Electrical Hydraulic Base Charge (q) Mass (m) Flow Current (I) Fluid flow (G) Potential Voltage (V) Pressure (p) Power P=IV P=Gp Lecture 1 2 Phasors • A phasor is a complex number that represents the magnitude and phase of a sinusoidal voltage or current: X M cost X X M Lecture 1 3 Class Examples • Extension Exercise 8.3 • Extension Exercise 8.4 Lecture 1 4 Complex Numbers Polar: z = A = x + jy : Rectangular imaginary axis • x is the real part • y is the imaginary part • z is the magnitude • is the phase y real axis x z x2 y2 x z cos y z sin tan Lecture 1 1 y x 5 Complex Number Addition and Subtraction • Addition is most easily performed in rectangular coordinates: A = x + jy B = 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 1 6 Complex Number Multiplication and Division • Multiplication is most easily performed in polar coordinates: A = AM B = BM f A B = (AM BM) ( f) • Division is also most easily performed in polar coordinates: A / B = (AM / BM) ( f) Lecture 1 7 Circuit Element Phasor Relations (ELI and ICE man) Element V/I Relation Phasor Relation Phase Capacitor I = C dV/dt I = j ω C V I leads V = ωCV 90° by 90º Inductor V = L dI/dt V = j ω L I V leads I by 90º = ωLI 90° Resistor V = I R V=RI In-phase = R I 0° Lecture 1 8 Class Examples • Extension Exercise 8.5 • Extension Exercise 8.6 • Extension Exercise 8.7 Lecture 1 9 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=IZ • Z is called impedance (units of ohms, W) • Impedance is (often) a complex number, but is not a phasor • Impedance depends on frequency Lecture 1 10 Impedance Summary Element Impedance Capacitor ZC = 1 / jC = -1/C 90 Inductor ZL = jL = L 90 Resistor ZR = R = R 0 Lecture 1 11 Series Impedance Z1 Z2 Zeq Z3 Zeq = Z1 + Z2 + Z3 Lecture 1 12 Parallel Impedance Z1 Z2 Z3 Zeq 1/Zeq = 1/Z1 + 1/Z2 + 1/Z3 Lecture 1 13 Class Examples • Extension Exercise E8.10 • Extension Exercise E8.8 Lecture 1 14