Transcription of Chapter 31 – Alternating Current - Physics
1 Chapter 31 Alternating Current - Phasors and Alternating Currents- Resistance and Reactance- Magnetic-Field Energy- The L-R-C Series Circuit- Power in Alternating - Current Circuits- Resonance in Alternating - Current Circuits- Transformers1. Phasors and Alternating CurrentstVv cos=Ex. source of ac: coil of wire rotating withconstant in a magnetic field sinusoidalalternating cos=v, i = instantaneous potential difference / , I = maximum potential difference / Current voltage/ Current amplitude. = 2 fPhasor Diagrams- Represent sinusoidally varying voltages / currents through the projection of a vector,with length equal to the amplitude, onto a horizontal Phasor:vector that rotates counterclockwisewith constant .Iirav 2=Rectified average Current (Irav): during any whole number of cycles, the total charge that flows is sameas if Current were constant (Irav).- Diode (rectifier): device that conducts better inone direction than in the other.
2 If ideal, R = 0 in one direction and R = in other. full wave rectifier circuitaverage value of cos t or sin t )2cos1( + =()tIIi +=2)(2 Iiiavrms==2 VVrms=Root-Mean Square (rms) values:tIi 222cos=2. Resistance and ReactancetVtIRiRvRR coscos)(===IRVR=Resistorin an ac circuit(instantaneouspotential)(amplitud e max- of voltage across R)- Current in phase with voltage phasors rotate togetherInductorin an ac CircuitdtdiL = - Current varies with time self-induced emf di/dt > 0 < 0 Va> Vb Vab= Va-Vb= VL= L di/dt > 0 () 90cossin)cos(+= ===tLItLIvtIdtdLdtdiLvLL vLhas 90 head start with respect to an ac circuit)90cos( +=tLIvL tIi cos=)cos( +=tVvLXL = = phase angle= phase of voltage relative to Current VLPure resistor: = 0 Pure inductor: = 90 LIIXVLL ==Inductive reactance:Voltage amplitude:LVIL =High low ILow high IInductors used to block high tIdtdqi cos==)90cos(sin ===tCItCICqvc Capacitorin an ac circuittIq sin=CIVC =As the capacitor charges and discharges at each t,there is i in each plate, and equal displacement currentbetween the plates, as though charge was conducted through C.
3 = tdtIdq cosC = q / vCPure capacitor: = 90 vclags Current by 90 .CXC 1=CCIXV=Capacitorin an ac circuitCapacitive reactance:CVIC =High high ILow low I(amplitude of voltage across C)Capacitors used to block low (or low f) high-pass filterComparing ac circuit elements:- R is independent of .- XLand XC depend on .- If = 0 (dc circuit) Xc= 1/ C ic= 0XL= L = 0 - If , XL iL= 0XC = 0 VC = 0 Current changes direction so rapidly that no charge can build up on each :amplifier C in tweeter branch blocks low-f components of soundbut passes high-f; L in woofer branch does the The L-R-C Series CircuitCCLLCIXVIXVIRV===- Instantaneous v across L, C, R = vad= v source- Total voltage phasor = vector sum of phasors ofindividual C, R, L in series same Current , i = I cos t only one phasor (I) for three circuit elements, amplitude The projections of I and V phasors onto horizontal axis at t give rise to instantaneousi and v.
4 (amplitudes = maximumvalues)222222)()()()(cLcLcLRXXRII XIXIRVVVV += += +=IZV=-The instantaneous potential difference between terminals a,d == algebraic sum of vR, vC, vL(instantaneous voltages) == sum of projections of phasors VR, VC, VL= projection of their vector sum (V) that represents the source voltage v and instantaneous voltage vadacross series of :22)]/1([CLRZ +=22)(cLXXRZ +=Impedance of R-L-C series circuit()RXXIRXXIVVVCLCLRCL = = = tanRCL /1tan =ZIV22=ZIVrmsrms=Phase angle of the source voltage with respect to Current () +=tVvcostIi cos=Example Power in Alternating - Current CircuitsVIP21=RVRIIVIVP rmsrmsrmsrmsav2222====VIP21=ttVItVItIttV tItVviP sincossincoscos]cos)][sinsincos(cos[]cos )][cos([2 = =+==Power in a General Circuit coscos21rmsrmsavIVVIP==5. Resonance in Alternating - Current CircuitsLCCLXXCL11000=== 6. TransformersdtdNdtdNBB = =2211 1212NN= )/(1212 NNRIV=1212 NNVV=
