Review_35-36-21-22

Review_35-36-21-22 - Chapter 36 Review AC Circuits Three...

Info iconThis preview shows pages 1–11. Sign up to view the full content.

View Full Document Right Arrow Icon
Chapter 36 Review AC Circuits
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Three categories of time behavior 1. Direct Current (DC) Voltages and currents are constants in time. Example: batteries - circuits driven by batteries 2. Transients Voltages and currents change in time after a switch is opened or closed. Changes diminish in time and stop if you wait long enough. S R L V 0 V L (t) t V L ( t ) = V 0 exp[ tR / L ]
Background image of page 2
3. Alternating Current (AC). The voltages and currents continually change sinusoidally in time. V ( t ) = V 0 cos[ ω t + θ ] amplitude frequency phase Examples: our power grid when it is on. f=60 Hz, V=110 V (RMS) audio signals communication signals Power in microwave ovens Power in MRI machines Real Life voltages involve DC, AC and Transients
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
AC - Circuits First Rule of AC - Circuits - everything oscillates at the same frequency The problem then becomes: Find the amplitude and phase of each voltage and current. Phasors - Everything you learned about DC circuits can be applied to AC circuits provided you do the following: 1. Replace all voltages and currents by their complex phasor amplitudes. In practice this means putting a hat on each letter. 2. Treat inductors as resistors with “resistance” j ω L 3. Treat capacitors as resistors with “resistance” 1/(j ω C)
Background image of page 4
I V 2 V 1 Foolproof sign convention for two terminal devices 1. Label current going in one terminal (your choice). 2. Define voltage to be potential at that terminal wrt the other terminal V= V 2 -V 1 3. Then no minus signs V = RI V = L dI dt I = C dV dt P = VI Power to device KVL Loop Contribution to voltage sum = +V
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Phasors for R-L circuit L Result: ˆ I = ˆ V 0 Z Impedance Z = R + jX L R V s (t) I(t) KVL V s ( t ) = Re ˆ V 0 e j ω t I ( t ) = Re ˆ Ie j ω t V L ( t ) = Re ˆ V L e j ω t V R ( t ) = Re ˆ V R e j ω t Write currents and voltages in phasor form KVL: 0 = ˆ V L + ˆ V R ˆ V 0 ˆ V L = j ( ω L ) ˆ I = jX L ˆ I ˆ V R = R ˆ I Write circuit equations for phasor amplitudes
Background image of page 6
Result: ˆ I = ˆ V 0 Z Impedance Z = R + jX L Impedance has a magnitude and phase Z = Z e j φ Z Z = R 2 + X L 2 tan φ Z = X L / R Z φ Z R X L Resistor Voltage ˆ V L = jX L ˆ I = ˆ V 0 jX L Z = ˆ V 0 X L Z e j ( π 2 φ Z ) ˆ V R = R ˆ I = ˆ V 0 R Z = ˆ V 0 R Z e j φ Z Inductor Voltage ˆ V 0 φ Z ˆ V R ˆ V L ˆ V 0 = ˆ V L + ˆ V R j = e j π 2 Note:
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
V L (t) I(t) t I( t ) = I 0 cos[ ω t + θ I ] V L = ω LI 0 sin[ ω t + θ I ] = ω LI 0 cos[ ω t + θ I + π 2 ] When I(t) is maximum V L (t) is zero and decreasing V L leads I by π /2
Background image of page 8
Power Dissipated in Resistor I( t ) = I R cos[ ω t ] p ( t ) = RI 2 = RI R 2 cos 2 [ ω t ] Current Instantaneous Power Average over time is 1/2 P = 1 2 RI R 2 Average Power
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Root Mean Square (RMS) Voltage and Current I( t ) = I R cos[ ω t ] Current P = 1 2 RI R 2 Average Power Peak current What would be the equivalent DC current as far as average power is concerned?
Background image of page 10
Image of page 11
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Page1 / 58

Review_35-36-21-22 - Chapter 36 Review AC Circuits Three...

This preview shows document pages 1 - 11. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online