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www.GOALias.blogspot.comAlternating Currentnot mean that the average power consumed is zero andthat there is no dissipation of electrical energy. As youknow, Joule heating is given by i 2 R and depends on i 2(which is always positive whether i is positive or negative)and not on i. Thus, there is Joule heating anddissipation of electrical energy when anac current passes through a resistor.The instantaneous power dissipated in the resistor is2 2 2p = i R= imRsinω t(7.4)The average value of p over a cycle is*2 2 2p =< i R >=< imRsinω t > [7.5(a)]where the bar over a letter(here, p) denotes its averagevalue and denotes taking average of the quantityinside the bracket. Since, i 2 and R are constants,m2 2p = imR < sin ωt> [7.5(b)]Using the trigonometric identity, sin 2 ωt =1/2 (1– cos 2ωt ), we have < sin 2 ωt > = (1/2) (1– < cos 2ωt >)and since < cos2ωt > = 0**, we have,< sin ω t > =2Thus,1 2p = i R[7.5(c)]2 12 mTo express ac power in the same form as dc power(P = I 2 R), a special value of current is defined and used.It is called, root mean square (rms) or effective current(Fig. 7.3) and is denoted by I rmsor I.George Westinghouse(1846 – 1914) A leadingproponent of the use ofalternating current overdirect current. Thus,he came into conflictwith Thomas Alva Edison,an advocate of directcurrent. Westinghousewas convinced that thetechnology of alternatingcurrent was the key tothe electrical future.He founded the famousCompany named after himand enlisted the servicesof Nicola Tesla andother inventors in thedevelopment of alternatingcurrent motors andapparatus for thetransmission of hightension current, pioneeringin large scale lighting.GEORGE WESTINGHOUSE (1846 – 1914)FIGURE 7.3 The rms current I is related to thepeak current i mby I = im/ 2 = 0.707 i m.1* The average value of a function F (t ) over a period T is given by Ft () = Ft () dtT∫T0T1 1 ⎡sin 2ωt ⎤ 1< cos 2 >= ∫ cos 2 = sin 2 0 0T T ⎢= − =⎣ 2ω⎥⎦ 2ωTT** ωt ωtdt [ ωT]0 0235