Alternating Current Notes PDF

CLASS 12 Alternating Current PHYSICS phasors...

CLASS 12 Alternating Current PHYSICS phasors 25 A phasor is a vector which rotates about Alternating Current and Alternating EMF An alternating current is one whose magnitude changes continuously with time between zero the origin with angular speed w and a maximum value and whose direction reverses periodically. The Vertical components of phasors V and I all opti will i represent the sinusoidally varying quantities is v and i. -> t alternating current is which varies with time simple harmonically. The simplest type of one AC voltage applied to a Resistor It is represented by i-isinet or i=iceset where it instantaneous value of current at time - we consider a source which produces sinusoidally varying maximum (or peak) value of the current and is called "Current Amplitude." its terminals. This potential difference i = otential difference ↑ across Angular Frequency (w) also called voltage, given by · where T= time period as ac W= 2IT=2177 T f = frequency. 1 = Vmsinut applying K2) and Law we get Alternating enf Ymsinct=iR i Imsinet · = = The comof (or voltage) whose magnitude changes continuously with time between zero and a maximum value and whose direction reverses periodically, is known as alternating emf. The instantaneous E= E sincet value of alternating or E= emit Ecosnt may be represented by Im= im so i= imsinut Note: The graphical representation of Eas sine and cosine functions of the are of the same form those of i #Graphical Representation as Amplitude maximum The alternating current varies in magnitude and reverses in direction periodically. The value of the current in either direction is called the "peak value" or the "amplitude" of the Sunil J current. It is represented by io a Periodic Time The time taken · by the alternating current to complete one cycle of variation is called the current is periodic-time" of the current. The periodic time 7 of the alternating given by ng NOTE: and Currents in phase with each other. T= 21T Voltage are To Phasor: A phasor is which rotates about the vector ra P ysics - a Frequency second is called the frequency origin with angular speed o The number of cycles completed by an alternating current in one ofthe current. Hertz (H2) cycles/second Phasor diagram Unit or F -> f or g = frequency = => the domestic alternating current t Note: The frequency of h is 30 cycles/second. Mean (or Average Value)* alternating current flows during one half-cycle in one-direction and during the An other in opposite direction. Hence, for one complete cycle, the mean value of alternating half-cycle # A.C voltage applied to a inductor current is zero. However, the mean value of alternating current over half a cycle is finite An Gu connected inductor. Let the are source to an voltage quantity and in fact, it is the quantity which is defined as the 'mean value of alternating across the source be V = Umsinct current. It is given by where i is the instantaneous value of the current. Apply ruji KC2, we get X-(diz0X = Ldi ↑mean=Yedt dE dE value i = isinut i peak = Ldi = xdt = Ldi = Umsinutdt T= 27T/c equation both side Tw Integrate above SLdi=/Umsintat FF fiolcossi-coson Mw Li Vncosnto ·mean a Sinutdt imean mCrot => = Pmean Cocoscut) - - - = Tw => T ⑳ where XECL 1msinkut-1T)"-cost-sinput-4) = imean io "mean =00637% imean-to 71-17 => or Inductive Reactance (Resistance and i=imsinpot-42) where in tam * = Lw= due to inductor unit of X2 is ohm (e). Root-men Square value NOTE: Current lags the voltage by IT/2. 9) is defined as that value of a direct current which produces the same amount of heating The average power supplied to inductor effect alternating in when over a given resistor as is produced by the given current passed an one complete cycle is LERO. for the same time during a complete cycle. 9 t is also called virtual value or effective value of A.C. Inductive Reactance (x2): -> Opposition offered by Instantaneous value of alternating current inductive circuit/inductor to the flow of Current. I = I sincet an Xz= (w= 2TTOL VazO for d02 X- 0 in time then if dH is small amount of heat produced at in Resistor R, Pac30H2 X,- Very large value, so inductor doc only. dH = Rdt (in one complete cycles passes is simtdt then total heat produced t An ac a generating ac voltage V Ymsincut source = HdH="/iRdt H = issintRat H => iR = connected to capacitor only, a purely capacitive ac circuit. a Let a be the charge on the capacitor at any time to the 1.2 ozwtdt instantaneous voltage across the Capacitor is H = iRptdt-Proszwed+ v = 8 applying KCI and Law "mSinct =9 cUmsinot = g = i H= iR (7-01 pirwt)I ieR/7-c/SinzwT-sinzwxos] - = H = Here T = LIT To find Current, we use =19+i=d (CUmsinart to · Ew i (UmCoscte T cost I=Umcost o Im = => = Te H = (RT -t(sin4T-sinol] it iRT H = - (i) where x= Capacitive Rectance (Resistance due to Capacitor) and Xc=//cw w=240 i =-incoscut current, and inSinut +it/) = NOTE: Current leads the voltage by 412 if Irms is rms value of alternating current and it is the heat produced by us then H= lEmsRT - (ii) NOTE: -> The average power supplied to an capacitor rms value of alternating emf. over one complete cycle is LERO from eq(i) and (ii) Erms =TrmsR E: IoR Capacitive Rectance (x2) Opposition lYmsRT IET · = offered by Erms R Fo = capacitive circuit Xc = 1 = 1 for de X20 = ⑧C GITVC Iris * Irms to F doe can't pass through I capacitors = 7Oo7f. of E ② So => Erms 0.7OFE. Eo = = trms= 00707 Io => Tums=7007% of fo Admittance (x)= Reciprocal of impedance Susceptance (S): Reciprocal of reactance is i.e x= defined susceptance. It is of two types. I as (i) inductive susceptance (ii) Capacitive susceptance SYL So To