Chapter 21 Alternating Current Circuits and Electromagnetic Waves 21 1 Resistors in an AC circuit DC circuit batteries as the power source V constant e g 1 5V AC circuit ac power source V Vmaxsin 2 ft It changes with time t f is the frequency 60 Hz in the US Canada and a few other countries with close ties to the US Average Pav i2R Imax 2R All powers we see on things e g light bulbs are average powers Vrms 110 V wall outlets Vmax 110 x 2 156 V Vrms IrmsR Vmax ImaxR vR iRR R is a constant for all frequencies 21 2 Capacitors in an AC circuit v lags i by 90o Early Vrms IrmsXC or Irms Vrms XC XC Capacitive Reactance XC 1 2 fC Unit 21 3 Inductors in an AC circuit v leads i by 90o Vrms IrmsXL XL Inductive Reactance X L 2 fL Unit The higher the frequency the higher the resistance Hard for current to go through and deal with self inductance at the same time Current lags v For HW get used to XL and XC having as unit and being functions of frequency Example A capacitor has a capacitance of 20 F What is its reactance when it is connected to a 100 Hz AC source If an inductor has the same reactance when connected to this source what is its inductance Two strange things about L and C The reactance depends on the frequency of the source Current and voltage don t go together 21 4 RLC Circuit The voice you hear from your cell phone is from this circuit same is true for all other wireless signals Current is the same for all components in series Vmax2 VR2 VL VC 2 Or Vrms2 VR rms2 VL rms VC rms 2 Using Vrms IrmsXL I rms Vrms Z tan XL XC R Vrms IrmsXL and Vrms Irms R Z R 2 X L X C 2 Phase angle For HW don t simply add resistance and reactance when they are in series Example Find the Vrms over R C and L 1 253320 H 1 x 10 8 F f 10 Hz Vrms 120 V 21 5 Power in an AC circuit L and C do not consume energy they only store energy Resistor is the only thing that consumes energy Two ways to calculate 21 6 Resonance in RLC Circuit If R 0 the circuit becomes LC circuit Vrms I rms X L X C 2 If XL XC I Large currents can be generated with small Vrms How wireless receivers work by receiving tiny Vrms Recall X L 2 fL XL XC 2 fL 1 2 fC XC 1 2 fC or f0 1 2 CL Vrms f0 Resonance Frequency I rms X L X C 2 At f0 Irms can be large with small Vrms Off f0 Irms is small f0 Every RLC circuit has its own resonance frequency f0 I Once an applied source has the same frequency it goes nuts f Hz 21 7 Transformers Increasing current in primary creates an increase in flux through primary and secondary Faraday s Law t Vs N s t iron Vp N p Vp V s Same t Vs N s Vp N p Energy conservation R NP primary NS secondary IpVp IsVs Transformers depend on a change in flux so they only work for alternating currents Example In Europe and most Asia outlets have 240 volts You need a transformer so you wrap 100 turns around the primary How many turns should you wrap around the secondary if you need 120 volts out to run your hair dryer Vs N s Vp N p V N s N p s 100 120 50 240 Vp Vp R V s NP primary NS secondary P IR2 on the power line The higher the voltage the smaller the current less power wasted Maxwell Equations physics at a new level Can be used for every problem we learned in electricity and magnetism and more EM waves Einstein The universe is highly mathematical with built in simplicity a glimpse of a mathematical God 21 10 Production of Electromagnetic waves Speed of light 299792458 m s Two rather trivial and UNRELATED constants 0 4 x 10 7 Tm A 1 2566371 x 10 6 Tm A 0 8 8541878 x 10 12 C2 Nm2 An AC current creates E field up and down I I I I I I 21 11 The Properties of Electromagnetic Waves Transverse wave oscillation perpendicular to the direction in which the wave travels Does not need medium to travel unlike sound waves I Emax Bmax 2 0 2 Emax 2 0 c 2 cBmax 2 0 Water molecule as receiving antenna Molecules as emitting antenna 21 12 The Electromagnetic Spectrum Light Radio TV Microwaves X Rays gamma ray Remember the Maxwell equations Good for all of them f c The echo of Creation peaks near 1 mm Arecibo Puerto Rico 21 13 The Doppler effect for EM waves EM waves are no different from other waves It diffracts like sound waves It shows Doppler effect Because the speed of sound is often much greater than that of emitters and listeners the equation can be simplified fo observed frequency fs source frequency u relative speed between the source and the observer for moving away and for approaching Other galaxies especially far away ones show as observed by Hubble the Hubble Flying away from us big bang Example How fast blue 400 nm red 660 nm