Co-operation with Europe

Abstract

WATTS AND VARSDear Sir-Two contributors to this correspondence support the view of the International Organization for Standardization (I.S.O.) that one var equals one watt, seven reject it. Those who support the I.S.O. reveal a misconception of the meaning of the technical term 'reactive power' and its unit, the var. They seem to believe that reactive power is the product of the voltage in a reactor and the current that flows in the reactor at the same moment of time. It is not. This quantity is not called reactive power and is not measured in vars, even if it occurs in a reactor or a capacitor. It is called power and is measured in watts.Reactive power is obtained by taking the product of two quantities that occur at different instants of time. In a 50c/s system these instants are separated by 1/2OOth of a second. When one multiplies a voltage that occurs at one instant of time by a current that occurs at another instant, the product is not a rate of change of energy, and I doubt whether any of the conflicting theories of dimensions could provide proof that a quantity that is not a rate of change of energy has, nevertheless, the dimensions of power.This argument is implicit in the contributions from many of your correspondents, but Mr. B. B. Jacobsen (October 1961 Journal, p. 604) comes nearest to removing the misconception. Let me repeat a little from his letter.Let the instantaneous value of a sinusoidally varying voltage be v = \/2 V sin cot and the instantaneous value of the current at the same moment of time be i = -\/2I sin (cot + <f>), where V and / are root-mean-square values. The product is: vi = VI(cos <j> -cos <j> cos 2cot + sin <j> sin 2cot) This shows that a constant power, VI cos <f>, which does not vary with time, is superimposed on an oscillating power that changes from moment to moment.It remains only to amplify Mr. Jacobsen's exposition. Let the instantaneous voltage v be multiplied by a current /', which occurs one quarter-cycle earlier than v. Then:i' = -\/2/ sin (cot 4-<f> - TT/2) and it is easy to show that:vi' = F/(sin <f> -sin <f> cos 2cot -cos <j> sin 2coi)

A late Pleistocene fauna from the Santa Elena Peninsula, Ecuador /

“…These are complexly faulted so that the precise structure is still in some doubt despite the accumulation of much data from well logs. References to the subsurface work are summarized in Marchant (1961).…”