Electric Power
I. Electric Power Generation
Electric Power is generated in
different forms. In the picture on the
left we can see how Electric Power
can be generated by the use of a
Hydroelectric Dam.
Other ways of generating Electric Power are: Nuclear power-generation, Fossil Fuel Generation,
Solar Cell Power generation, Wind Power, Geo-Thermal Power, Chemical Power(as in a Battery).
For more information see: www.tva.gov/power.
II. Electric Power: P = I*V
A cloud of Charge Q exhibits a Potential of V .
Electrical Energy is defined as the Energy spent
to move the Charge Q through the potential difference
of V, or E = Q*V.
Electric Power is the rate at which Energy is spent, or P = E/T. Since the Units of Energy are Joules,
the Units of Power are Joules/second or Watts where 1W = 1J/s.
Writing out the whole equation we get P= (Q*V)/T, but since Q/T is the definition for current (Current is
the charge flowing per unit time) we have that P = I*V which is the Basic Power Formula. Note that this
Formula also tells us that I = P/V and V= P/I.
Circuit Example:
We want to know the Power delivered by the circuit on
the left and the current through the resistor once the switch
S1 is closed. First, I = V/R = 10V/10Ohms = 1 Amp.
Then, P= I*V = 1Amp* 10V = 10 Watts = 10W
III. Power and Resistance
A light bulb that glows is a resistor dissipating power through heat. So do any other type of resistors dissipate
power and according to their markings some can dissipate only a maximum of 1/4 Watt or 1/2 Watt
respectively. In the circuit example given above we could have found the power directly associated with the
resistor by noting that if I = V/R then by substitution P = V * I or P = V * V/R or P = V2 /R.
Now, suppose that we have a basic circuit where the current and the resistance are given, but the voltage is
unknown. Suppose, we have I = 5 Amps and R = 10 Ohms. Here, we could first use Ohm's Law to obtain
the voltage and then the Basic Power Formula to obtain the power dissipated through the resistor.
But again, note that since V = I*R, by substitution we can express P = V*I or P = I*R*I or P = I2*R.
Consequently: We have two formulas for power across a resistor:
1. P = V2 /R and 2. P = I2*R.
Note: The first formula gives us two additional equations: V = Sqrt(P*R) and R = V2/P.
The second formula also gives us two additional equations: I = Sqrt(P/R) and R = P/I2.
For Quick Reference: We can have formulas 1. and 2. expressed in a "circle" fashion :
Where if we cover one of the segments of the circle, the remaining segments will give us the right formula.