Ch+21+-+AC+Circuits

  Cdubz Dibs //In this chapter such concepts as resistors, capacitors, and inductors in an AC circuit, RLC circuits, power, resonance, the transformer, Maxwell's predictions, Hertz's Confirmation, and electromagnetic waves.//
 * Chapter 21 ** **: Alternating Current Circuits and electromagnetic Waves **


 * [[image:Untitled3.png width="148" height="63"]]

AC VS DC** AC Current is more efficient and is able to be carried over long distances Eddison backed DC Current and thought of a battery outside of the house

//this diagram shows a plot of current and voltage across a resistor provided in the book on page 653// Voltage across the resistor is in phase with the current ∆VR//,rms//= I//rms//R
 * Resistors in an AC Circuit:**

I//rms//= (I//max//)/(√2)= 0.707I//max// ∆V//rms//=(∆V//max//)/(√2)= 0.707∆V//max//

Rms voltage across resistor = rms current in the circuit * resistance

With charge: as voltage increases, current decreases and vise versa //this diagram shows a plot of current and voltage across a capacitor provided in the book on page 656// Voltage across a capacitor awlays lags behind current by 90º ∆V//C,rms//= I//rms//X//c//
 * Capacitors in an AC Circuit:**

Capacitive Reactance: X//c//=1/(2π//f//C), units=Ω Impeding Effect Capacitance Reactance:
 * At high frequency- less time to charge capacitor so less charge and voltage accumulate

V//inst//=L(∆I/∆t) Changing current produces a back EMF which impedes the current in the circuit //this diagram shows a plot of current and voltage across a capacitor provided in the book on page 657// Voltage across an inductor always leads the current by 90º ∆V//L,rms//= I//rms//X//L//
 * Inductors in an AC Circuit:**

Inductive Reactance: X//L//= 2π//f//L

Rotating vector is considered the phasor which is part of a phasor diagram //(diagram below from book page 659)// //Rotating around at frequency (in normal household 60Hz)//
 * RLC Series Circuit:**

Impedance: Z= √(R²+(X//L//-X//c//)²) ∆V//max//= I//max//Z tanø= (X//L-//X//c//)/R

The table below shows the Impedance Values and Phase Angles for Certain Series Circuit Combinations provided in the book on page 661 The diagram below shows phase relations in RLC series circuits provided from page 659 from the book Voltage in //c// is in lead of the current Voltage in //d// in lagging behind the current ELI (voltage leads the current for and inductor) ICE (current leads voltage for capacitor)

resonance frequency://f0//= 1/ (2π(√LC))
 * Resonance:**
 * //this frequency occurs when XL=XC, therefore the impedance reduces to Z=R//

P//av//= I²//rms//R P//av//= I//rms//∆V//rms//*cosø ø= power factor
 * Power in an AC Circuit:**
 * RMS- root, mean, squared**


 * Reversing Current:**
 * V=iR
 * P=i2R
 * Square of the current reverses the direction

The transformer can be used to step up or step down voltage. Primary Coil- where voltage is applied (induced voltage) ∆V1= -N1(∆IB/∆t) Secondary Coil- where voltage is produced ∆V2= -N2(∆IB/∆t)
 * The Transformer:**

∆V2= (N2/N1)*∆V1 I1∆V1=I2∆V2

//this diagram shown on page 665 of the book shows how an ideal transformer has an iron core with two coils (primary and secondary) wrapped around itself and then as AC voltage is appled to ∆V1 a different voltage is produced on ∆V2//

//Example Lab From Our Class: Step Down Transformer Setup: Step Up Transformer Setup: //

"A changing E field can produce a B Field - Symmetry**"-**Mr Smith Predictions: >
 * Maxwell's Predictions:**
 * Electric field lines start on positive and end on negative
 * Magnetic field lines are always closed loops
 * Changing magnetic field induces and emf and therefore and electric field. (clarifies Faraday's law)
 * Moving charges (currents) create magnetic fields (Ampères Law)

Properties traveling through free space:
 * Electromagnetic Waves:**
 * Electromagnetic waves travel at the same speed as that of light (3*10⁸m/s)
 * The electric and magnetic fields are perpendicular to each other and the direction of propagation, which therefore infers that these waves are categorized as transverse waves
 * The ratio of magnetic and electric field is equal to the speed of light
 * Electromagnetic waves carry energy and momentum, which is then transferred to mediums

c= 1/(√(µ0e0) c~ 2.99792*10⁸m/s E/B=c

Average power per unit area= EmaxBmax/(2µ0) = E²max/(2µ0c) = (c/(2µ0))*B²max Complete Absorption: p=U/c Complete Reflection: p= 2U/c

ap class blog from 02-28-08