530_343lecture15

# 530_343lecture15 - ME 530.343 Design and Analysis of...

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ME 530.343: Design and Analysis of Dynamic Systems Spring 2009 Lecture 15 - Electrical Systems as Dynamic Systems Wednesday, April 8, 2009 Today’s Objectives Develop dynamical equations for electrical systems Reading: Palm Chapter 6 Variables most common: e , voltage (V, volts) i , current (A, amperes) related variables: q , charge (C, coulombs) φ , ﬂux (Wb, Webers) Λ, ﬂux linkage (Weber-turns) relationships: i = dq dt q ( t ) = q ( t 0 ) = R i ( λ ) Λ = ( N = # of turns in a coil of wire) Elements Resistors Ohm’s Law: e = Ri , i = 1 R e R = resistance in ohms (Ω) For a body of length l , cross-sectional area A and material resistivity ρ , R = ρl A A resistor dissipates energy, so power is p = ei = Ri 2 = 1 R e 2 1

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Capacitor Creates a relationship between voltage and charge C = capacitance in Farads (F) q = Ce i = C de dt e ( t ) = e ( t 0 ) + 1 C R i ( λ ) Physical form: two parallel metallic plates, each of area A , separated by a dielectric material of thickness
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530_343lecture15 - ME 530.343 Design and Analysis of...

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