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(ELEC101)tutorial06.pdf
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Tutorial 06 --
AC Circuit

Fall 2006
ELEC101 BASIC ELECTRONICS


Outline

.Basic

.VI Relationship of R, C and L

.Complex Method

.Complex Method for AC Circuit




Basic



Basic



VI Relationship of Resistor



VI Relationship of Inductor




VI Relationship of Capacitor

C

I(t) = Im cos t
V(t) = 1/C i(t) dt
= 1/C (Im cos t) dt
= (1/C) (Im sin t)
= (Im/C) (sin t)
= (Im/C) cos (90o-t)
= Vm cos (t -90o)

Capacitor (C) or capacitiveelement (C with R) is also called leading element.


Text Box: . I > . V , I leads V
Text Box: . I = 0, . V = - 90o,

Complex Method

a: real part
b: imaginary part


Text Box: D. Polar form : w = M..
Text Box: C. Exponential form: w = M e j .
Text Box: Complex conjugate = w* = a - jb = = M e -j . = M.- .



Complex Method




Complex Method



Complex Method



Analyzing AC Circuit

Assumptions:
1. The circuit is in steady state
2. The circuit contains sinusoidal V and I sources with the same frequency


Complex Method for AC Circuit

Text Box: Transform voltages and currents with same frequency to complex V and I phasors. 2. Transform L, C, R elements to complex impedance Z (or transform to complex admittance Y).3. Apply network theorems to solve the complex V and I.

Complex Method for AC Circuit

Transform v(t), i(t) to Phasor V, I

1.Express v(t) and i(t) with same to VMcos (t +v) and
IMcos (t +I) form
2. Convert the cosine form into phasor V and I form
VMe jv or VMv and IMe jIor IMI
3. After the circuit analysis, convert the phasor V and I form
back to v(t) and i(t)

Example: find phasor V