1 / 19

Announcements

Announcements. Assignment 0 due now. solutions posted later today Assignment 1 posted, due Thursday Sept 22 nd Question from last lecture: Does V TH =I N R TH Yes!. Lecture 5 Overview. Alternating Current AC Components. AC circuit analysis. pure DC. V. pulsating DC. V.

cheng
Download Presentation

Announcements

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Announcements • Assignment 0 due now. • solutions posted later today • Assignment 1 posted, • due Thursday Sept 22nd • Question from last lecture: • Does VTH=INRTH • Yes!

  2. Lecture 5 Overview • Alternating Current • AC Components. • AC circuit analysis

  3. pure DC V pulsating DC V pulsating DC V AC V -V Alternating Current • pure direct current = DC • Direction of charge flow (current) always the same and constant. • pulsating DC • Direction of charge flow always the same but variable • AC = Alternating Current • Direction of Charge flow alternates

  4. Why use AC? The "War of the Currents" • Late 1880's: Westinghouse backed AC, developed by Tesla, Edison backed DC (despite Tesla's advice). Edison killed an elephant (with AC) to prove his point. • http://www.youtube.com/watch?v=RkBU3aYsf0Q • Turning point when Westinghouse won the contract for the Chicago Worlds fair • Westinghouse was right • PL=I2RL: Lowest transmission loss uses High Voltages and Low Currents • With DC, difficult to transform high voltage to more practical low voltage efficiently • AC transformers are simple and extremely efficient - see later. • Nowadays, distribute electricity at up to 765 kV

  5. AC circuits: Sinusoidal waves • Fundamental wave form • Fourier Theorem: Can construct any other wave form (e.g. square wave) by adding sinusoids of different frequencies • x(t)=Acos(ωt+) • f=1/T (cycles/s) • ω=2πf (rad/s) •  =2π(Δt/T) rad/s •  =360(Δt/T) deg/s

  6. RMS quantities in AC circuits • What's the best way to describe the strength of a varying AC signal? • Average = 0; Peak=+/- • Sometimes use peak-to-peak • Usually use Root-mean-square (RMS) • (DVM measures this)

  7. i-V relationships in AC circuits: Resistors Source vs(t)=Asinωt vR(t)= vs(t)=Asinωt vR(t) and iR(t) are in phase

  8. 2 2 Complex Number Review Phasor representation

  9. i-V relationships in AC circuits: Resistors Source vs(t)=Asinωt vR(t)= vs(t)=Asinωt vR(t) and iR(t) are in phase Complex representation: vS(t)=Asinωt=Acos(ωt-90)=real part of [VS(jω)] whereVS(jω)= A[cos(ωt-90)-jsin(ωt-90 )]=Aej (ωt-90) Phasor representation: VS(jω) =A(ωt-90) IS(jω)=(A/R) (ωt-90) Impedance=complex number of ResistanceZ=VS(jω)/IS(jω)=R Generalized Ohm's Law: VS(jω)=ZIS(jω) http://arapaho.nsuok.edu/%7Ebradfiel/p1215/fendt/phe/accircuit.htm

  10. Capacitors What is a capacitor? Definition of Capacitance: C=q/V Capacitance measured in Farads (usually pico - micro) Energy stored in a Capacitor = ½CV2 (Energy is stored as an electric field) In Parallel: V=V1=V2=V3 q=q1+q2+q3 i.e. like resistors in series

  11. Capacitors In Series: V=V1+V2+V3 q=q1=q2=q3 i.e. like resistors in parallel No current flows through a capacitor In AC circuits charge build-up/discharge mimics a current flow. A Capacitor in a DC circuit acts like a break (open circuit)

  12. Capacitors in AC circuits Capacitive Load "capacitive reactance" • Voltage and current not in phase: • Current leads voltage by 90 degrees (Physical - current must conduct charge to capacitor plates in order to raise the voltage) • Impedance of Capacitor decreases with increasing frequency http://arapaho.nsuok.edu/%7Ebradfiel/p1215/fendt/phe/accircuit.htm

  13. Inductors What is an inductor? Definition of Inductance: vL(t)=-LdI/dt Measured in Henrys (usually milli- micro-) Energy stored in an inductor: WL= ½ LiL2(t) (Energy is stored as a magnetic field) • Current through coil produces magnetic flux • Changing current results in changing magnetic flux • Changing magnetic flux induces a voltage (Faraday's Law v(t)=-dΦ/dt)

  14. Inductors Inductances in series add: Inductances in parallel combine like resistors in parallel (almost never done because of magnetic coupling) An inductor in a DC circuit behaves like a short (a wire).

  15. Inductive Load Inductors in AC circuits (back emf ) from KVL • Voltage and current not in phase: • Current lags voltage by 90 degrees • Impedance of Inductor increases with increasing frequency http://arapaho.nsuok.edu/%7Ebradfiel/p1215/fendt/phe/accircuit.htm

  16. AC circuit analysis • Effective impedance: example • Procedure to solve a problem • Identify the sinusoid and note the frequency • Convert the source(s) to complex/phasor form • Represent each circuit element by it's AC impedance • Solve the resulting phasor circuit using standard circuit solving tools (KVL,KCL,Mesh etc.) • Convert the complex/phasor form answer to its time domain equivalent

  17. Example

  18. Top: Bottom:

More Related