MadSci Network: Engineering

Re: What is power, apparent & reactive conceptually. Does power flow or energy.

Date: Fri Jul 23 08:19:36 1999
Posted By: Lawrence Skarin, Faculty, Electrical Engineering, Monroe Community College
Area of science: Engineering
ID: 932659334.Eg

If you roll a 50 pound stone up a hill 5 feet, and take 10 seconds to do it, 
you have added 250 pound-feet of energy to the stone, and applied 25 pound-feet 
per second of power for 10 seconds.  Power is the time rate of energy 
transfer.  Calculus-savvy people would say power is the time derivative of 

Direct Current (DC) came first; Alternating Current (AC) came later.  In DC, 
you multiply voltage difference times amperes to find power.  The energy is 
power times time in seconds.  In calculus, energy is the time integral of power.

For AC, there is an additional consideration.  Sinewaves of voltage and current 
have amplitudes in volts and amperes, but the sinewaves need not peak at the 
same time.  The phase angle difference between the peaks is called THETA.  For 
historic reasons, the amplitudes of voltage and current are in a unit called 
root-mean-squared volts and amperes.  Thus:

Apparent Power = V*I

True or Real Power = V*I*cosine(THETA)

Reactive or Imaginary Power = V*I*sine(THETA)

The electric watt-hour meter read by a utility is an electromechanical 
integrator that time-integrates the true power.  Reactive power goes through 
the meter with no effect on the accumulated reading.  But do not, by this fact, 
believe that utilities are not interested in reactive power and billing for its 
consequences.  The electric company must size its transformers and other 
facilities based on current -- not power.  Therefore (and there are ways) 
reactive power is often measured and taken into account for billing purposes.

Hope this helps.

Larry Skarin
Power is to energy as speed is to distance.  You can't transfer energy without 
having power just like you can't go a distance without having a nonzero speed 
in some direction.

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