Electric Energy & Power

Energy is defined as the amount of work done on an object.  Energy is the ability to do work.

Electric Energy is the ability of a power source to move electrons in a closed circuit and do work on a load.   This amount of work is converted by the load into useful energy. Alight bulb will produce light and heat.  A motor will produce torque and mechanical energy.  A resistor will slow down electrons to produce heat, an a speaker will convert electrical impulses into sound energy.  These are some examples of electric energy-work conversions in a  circuit.

The Energy used in a circuit depends on the amount of voltage (or the "push" that the electrons get at the source) and the charge on the electrons.

Summarizing these factors in a simple formula:

Energy = Charge x Voltage

          E = Q x V

the respective units are:
Joules = Coulombs x Volts

We can also express the charge in terms of the current. 

Recall that current was given by the formula I = Q / t   or by rearranging ... Q = I x t

Therefore,  we can express the Energy used by a circuit (or a load) in terms of voltage and current used by the load or produced by a voltage source.

E = Q x V  =  I x t x V

Often the energy of a battery or power source is express in Volt-Amp-hours (an expression derived from the above formula)

Electric Power

We define power as the rate at which work is done or the rate at which energy is used.  In symbols this expression can be written as:

In electric circuits we often need to know how much power a source produces or a load uses.

We can rewrite the above expression to fit the requirements of electric circuits using voltage and current using the above equations.

The symbol for power is P and the units are Watts.  one watt is equal to one Joule per one second

or in symbolic form:    

Alternative Units:

1. The horse power (HP)-- an alternative power unit.
    When James Watts perfection the steam engine for commercial applications it was not a very successful product at first because people did not understand how powerful it really was.  The unit of power he used (The Watt) meant very little to farmers and other entrepreneurs.  Watts realized that he had to find a unit of power that people could understand in relation to their everyday use.    He measured the power a horse could develop in lifting a certain load and called it ONE HORSE POWER.   He then used the power of his steam engine to lift the same load and found that it took about 746 Watts to lift the same amount of load.

   The unit of the horsepower now represented a real quantity that people could understand and relate to;

   This conversion is still in use today
    1 Horsepower = 746 Watts.

    

2. The kilowatt-Hour (kWHr) -- an alternative energy unit.
   The Joule is small unit for large scale, commercial, residential, industrial and other practical applications.
   Electrical energy consumption is measured and billed in how much usage occurs over several days (one month billing periods are usually the norm).  Thus the need for an energy unit that would measure consumption of several thousand watts of power over many hours of usage.
   The kilowatt-hour measures the energy consumption based on this large scale usage.

How many joules are there in 1 kilowatt-hour?
1kW = 1 000 W
1 hr = 60 min/hr x 60 s/min = 3 600 s
\ 1 kWhr = 1 000 W x 3 600 s
             = 3 600 000 W s 
but 1 W = 1 J/s \ 1 W s = 1 J
\ 3 600 000 W s = 3 600 000 J

\ There are 3 600 000 J in 1 kWhr

Note that 3 600 000 J  can also be written as 3.6 x 10 ⁶  J or 3.6 MJ ("mega joules").

Exercises