Phys 345 Electronics for Scientists - Delaware Physics

Phys 345 Electronics for Scientists - Delaware Physics

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

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

V Direction of Charge flow alternates -V AC 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 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(t+) f=1/T (cycles/s) =2f (rad/s) =2(t/T) rad/s =360(t/T) deg/s 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)

I rms Ip 2 , Vrms Vp 2 , Pave I rmsVrms i-V relationships in AC circuits: Resistors Source vs(t)=Asint vR(t)= vs(t)=Asint iR (t )

vR (t ) A sin t R R vR(t) and iR(t) are in phase Complex Number Review Phasor representation 2 2 i-V relationships in AC circuits: Resistors Source vs(t)=Asint vR(t)= vs(t)=Asint

iR (t ) vR (t ) A sin t R R vR(t) and iR(t) are in phase Complex representation: vS(t)=Asint=Acos(t-90)=real part of [VS(j)] where VS(j)= A[cos(t-90)-jsin(t-90 )]=Aej (t-90) Phasor representation: VS(j) =A(t-90) IS(j)=(A/R) (t-90) Impedance=complex number of Resistance Z=VS(j)/IS(j)=R Generalized Ohm's Law: VS(j)=ZIS(j) Capacitors What is a capacitor? Definition of Capacitance: C=q/V Capacitance measured in Farads (usually pico - micro)

Energy stored in a Capacitor = CV2 (Energy is stored as an electric field) In Parallel: V=V1=V2=V3 q=q1+q2+q3 q q1 q2 q3 Ceq C1 C2 C3 V V i.e. like resistors in series Capacitors In Series: V=V1+V2+V3 q=q1=q2=q3 1 V V1 V2 V3 1

1 1 Ceq q q C1 C2 C3 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 Capacitors in AC circuits Capacitive Load

vC A sin t qC CvC dqC CA cos(t ) dt VC ( j ) A(t 90) iC I C ( j ) CA(t 0) ZC VC ( j ) 1 90 C I C ( j ) cos( 90) j sin( 90) j

j j. j 1 C jC jC "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 Inductors What is an inductor? Definition of Inductance: vL(t)=-LdI/dt Measured in Henrys (usually milli- micro-) Energy stored in an inductor: WL= 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)=-d/dt) 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). Inductors in AC circuits Inductive Load

vS A sin t vL L diL dt A sin t L (back emf ) diL dt from KVL A A iL sin tdt cos t L L

A A iL sin(t 90) cos(t 180) L L VL ( j ) A(t 90) A (t 180) L V ( j ) ZL L L90 I L ( j ) cos(90) j sin(90) j Z L j L I L ( j ) 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 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

Example ( Z R1 Z C ) I1 ( j ) Z C I 2 ( j ) VS ( j ) Z C I1 ( j ) ( Z C Z L Z R 2 ) I 2 ( j ) 0 VS ( j ) ZC 0 ZC Z L Z R2 ( Z C Z L Z R 2 )VS ( j ) I 1 ( j ) 2 Z R1 Z C ZC ( Z R1 Z C )( Z C Z L Z R 2 ) Z C

ZC ZC Z L Z R2 1 1 66.7 66.7 j () 6 jC j1500 10 j Z L jL j1500 0.5 750 j () ZC (75 683 j )150 I 1 ( j ) (100 66.7 j )(75 683 j ) 4450 (75 683 j )150 I 1 ( j )

(100 66.7 j )(75 683 j ) 4450 Top: Bottom: (75 683 j )150 68783.7 150 tan 1 b 683 tan 1 83.7 a 75 A a 2 b 2 687 (100 66.7 j )(75 683 j ) 4450 7500 45600 5000 j 683 j 4450 57550 63300 j 8550047.8

68783.7 150 I 1 ( j ) 8550047.8 0.1235.9 0.120.63 radians i1 (t ) 0.12 cos(1500t 0.63) Amps

Recently Viewed Presentations

  • Computational Physics - BGU

    Computational Physics - BGU

    Computational PhysicsNumerical Differentiation. Dr. Guy Tel-Zur. Clouds. Picture by Peter Griffin, publicdomainpictures.net. MHJ Chapter 3: Numerical Differentiation. Should be f'c "2" stands for two points. forward/backward 1st derivative: ±h . f(x)=a+bx^2.
  • The Shell Method - Welcome to Mrs. Nykamp's Class!

    The Shell Method - Welcome to Mrs. Nykamp's Class!

    The Shell Method. Section 7.3. Find the Volume. Use the disk/washer method to find the volume of the solid generated by revolving the plane region about the y-axis. Region bounded by ?=4?−?2 and ?=0. ...
  • Constraining Generalisation in Artificial Language Learning: Children are

    Constraining Generalisation in Artificial Language Learning: Children are

    Elizabeth Wonnacott,1 Amy Perfors..2 University of Oxford 1,University of Adeleaide2 [email protected] 1. Abstract 5. Results 3. Experiments Successful language acquisition involves generalization, but learners must balance this against the acquisition of lexical constraints. Examples occur throughout language.
  • AERODYNAMICS - OpenCourseWare

    AERODYNAMICS - OpenCourseWare

    The front end should start at a low stagnation line, and curve up in a continuous line. The front screen should be raked as much as is practical. All body panels should have a minimal gap. Glazing should be flush...
  • Presentation Title

    Presentation Title

    Technologically simple or unsophisticated, and readily available in most offices (e.g., replacing a door knob with an accessible door handle, providing a magnifier). High-tech: Advanced or sophisticated devices (screen reading software with synthesized speech).
  • New CountrySTAT approach

    New CountrySTAT approach

    The current version, CPC version 2.1, is the result of a scheduled review of the CPC structure and detail, in order to ensure the classification's relevance for describing current products in the economy.
  • Justice, Peace and Development Commission Listening Exercise -

    Justice, Peace and Development Commission Listening Exercise -

    Target was 150 responses from each area. Background - Response to the process. 450 questionnaires were distributed, 322 were completed. ... the difficulty attending Mass with small children, the sense that they are not welcome because their lifestyle choice is...
  • The Road to WWII American Isolationism  Following WWI,

    The Road to WWII American Isolationism Following WWI,

    The Nye Committee's report implied that certain businesses had profited from the war, leading many American's to believe that they had been tricked into entering WWI. Again, this encouraged American support of isolationism. Congress created a special committee in 1934...