Review_35-36-21-22

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

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

Chapter 36 Review AC Circuits

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

View Full Document
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 ]
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

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

View Full Document
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)
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

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

View Full Document
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
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:

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

View Full Document
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
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

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

View Full Document
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?
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 12/28/2011 for the course PHYSICS 270 taught by Professor Drake during the Fall '08 term at Maryland.

### 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
Ask a homework question - tutors are online