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CHAP. VI POWER, IN ALTERNATING-CURRENT CIRCUITS 57

the components K COH$ and K Bin fa in phase and in quadrature
with the current, In this ease, oq. (77) in exprensed in words by
Baying that the average power in equal to the cxirrent times the
component of the* voltage in phanc with it. Those components
of the voltage art* also called the energy component and the reactive
component respectively* The two component** of power, the true
power A7eos#, and the reactive power KImifa stand in the
name relation to the apparent power Kl an the two sides of a
right triangle bear to the hypotenuse; that in,

( Kl )* { Kl COM $)* +< (A7 Kin ^ ..... (78)

Let now the current and voltage curves be different from pure
Hiuo-waveH, and also different from each other in form. The
fundamental equation

(I IT] f

«/o

^Tei-dt ..... (79)

holds true in all eases, HO that if the curves are given graphically,
the energy per cycle in found by multiplying the corresponding
instantaneous values* of r anil t\ and using the planimeter on the
resultant curve. The average ordinal e of this curves given the
average power, Of course, the parts of the rcHultaut curve below
the axis of alwissH* must bo evaluated separately from those above
it, and the difference of the two taken to represent the total

If the two wavert lire given in the form of Fourier BorieB, an
exprcHSum for the nveraw power may be obtiuncnl in terme of
the effective valu«*H of the itannonioH. HubKtituting the expan-
Htoim for c nwi i into eq» (70), two kindw of terms are obtained,-—
thane containing pr«itlti«^ftH of two hannouu*s of the natne frequency,
and thorte coiitaiiiiiig pnwhi«*tH of two tmrmonitm of different fro-
^* The trruw of the llrnt kind» after integration, give re-
tif th«« HHUW* fnritt us for the fiiiidiwnental wave; that in, for
the wth hiifiituiiir | AVu «'<»>* *«• where A'_H and /« are the amplituden
of the ttth hiirtuuinrN, niitl $* U tin* phtwe dwplacMiient between
them. The twun 4 if tin* m^nul kind give zero after integration,
the proof of this being liiinloginw to thut in problem 3 of thf pre-
ceiting article. Thiw

/*,„. "" i KJ\ niH^i f i ^yieos^s + etc. . . (HO)
In cither w«*r*k rwh tin own atore of power,

m if il tri?/*r



	CHAP. VI POWER, IN ALTERNATING-CURRENT CIRCUITS 57 the components K COH$ and K Bin fa in phase and in quadrature with the current, In this ease, oq. (77) in exprensed in words by Baying that the average power in equal to the cxirrent times the component of the* voltage in phanc with it. Those components of the voltage art* also called the energy component and the reactive component respectively* The two component** of power, the true power A7eos#, and the reactive power KImifa stand in the name relation to the apparent power Kl an the two sides of a right triangle bear to the hypotenuse; that in, ( Kl )* { Kl COM $)* +< (A7 Kin ^ ..... (78) Let now the current and voltage curves be different from pure Hiuo-waveH, and also different from each other in form. The fundamental equation

	(I IT] f «/o	^Tei-dt ..... (79)

	holds true in all eases, HO that if the curves are given graphically, the energy per cycle in found by multiplying the corresponding instantaneous values* of r anil t\ and using the planimeter on the resultant curve. The average ordinal e of this curves given the average power, Of course, the parts of the rcHultaut curve below the axis of alwissH* must bo evaluated separately from those above it, and the difference of the two taken to represent the total

	If the two wavert lire given in the form of Fourier BorieB, an exprcHSum for the nveraw power may be obtiuncnl in terme of the effective valu«H of the itannonioH. HubKtituting the expan- Htoim for c nwi i into eq» (70), two kindw of terms are obtained,-— thane containing pr«itlti«^ftH of two hannouus of the natne frequency, and thorte coiitaiiiiiig pnwhi«tH of two tmrmonitm of different fro- ^ The trruw of the llrnt kind» after integration, give re- tif th«« HHUW* fnritt us for the fiiiidiwnental wave; that in, for the wth hiifiituiiir \| AVu «'<»>* «• where A'_H and /« are the amplituden of the ttth hiirtuuinrN, niitl $ U tin* phtwe dwplacMiient between them. The twun 4 if tin* m^nul kind give zero after integration, the proof of this being liiinloginw to thut in problem 3 of thf pre- ceiting article. Thiw /,„. "" i KJ\* niH^i f i ^yieos^s + etc. . . (HO) In cither w«rk rwh tin own atore of power, m if il tri?/*r