Final Exam Study Sheet

Final Exam Study Sheet - Phasor Form Vs = Vrms<theta...

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Final Exam Study Sheet A. Review Study sheets for Exams 1 and 2 B. Topics from Ch. 14, 15, 16, and 18 (Robbins & Miller) Ch. 14 Inductive Transients for an inductor: v = L di/dt for steady state (nothing changing) di/dt = 0, therefore vl = 0 V for series R and L: time constant, tau = L/R and switch closes at t = 0 s since at t = 0- s, i is, by definition, = 0 A then i = 0 A at t = 0 s and at t = 0+ s, and vr also = 0 V i = (Vs/R)*(1 - e^(-t/tau)); = Vs/R at t = inf or 5 tau vr - iR = Vs*(1 - e^(-t/tau)); = Vs at t = inf or 5 tau vl = Vs - vr = Vs(e^(-t/tau); = 0 at t = inf or 5 tau ================================== Ch. 15 Intro to AC vs = Vp sin wt in the time domain where Vp = peak voltage of sine wave w = angular frequency in rad/s f = frequency in Hz = w/2pi T = period = 1/f in s Vpp = peak-to-peak voltage = 2Vp T is equivalent to 2pi radians and is equivalent to 360 degrees vs = Vp sin (wt +/- theta) where theta is phase shift typically given in degrees and if -, is said to be lagging and, if +, is said to be leading another signal that has theta = 0.
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Unformatted text preview: Phasor Form: Vs = Vrms <theta where Vrms = 0.707*Vp and is said to be the effective value. The rms value of a dc voltage is equal to its dc value. Ch. 16 Impedance Complex Numbers: form is A +/- jB in rectangular format, where j = sqrt(-1) form is M<theta in polar format M = sqrt(A^2 + B^2) and theta = arctan (B/A) A = M cos(theta) and B = M sin(theta) for a capacitor: since i = C dv/dt and if v = Vp sin(wt0 then i = C*w*Vp*cos(wt) = C*w*Vp*sin(wt + 90deg) where C*w*Vp = Ip and Vp/Ip = 1/wC = 1/(2*pi*f*C) = Xc<-90deg Xc is called the reactance of the capacitor for an inductor it can be shown that: Xl = wL = 2*pi*f*L = Xl<+90deg Ch. 18 Series R,L, C circuit: impedance = Z = R +jXl -jXc = R +j(Xl - Xc) in rectangular form and the units are ohms. for a given Vs, i = Vs/Zt and Vr = iR, Vc = i*Xc and Vl = i*Xl where all work must be done using complex numbers in either rectangular or polar format....
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This note was uploaded on 12/14/2010 for the course ECET 107 taught by Professor Huehne,karl during the Spring '09 term at IUPUI.

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Final Exam Study Sheet - Phasor Form Vs = Vrms<theta...

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