Dynamic Electricity: Electric Energy &Power

Electric Power The electric power of a machine is an indication of the amount of work it can do, that is, the amount of energy it can transform in a certain amount of time. Therefore, the more powerful a machine, the faster it works. Also, the more work it can do in a set period of time, the more powerful it is.

Power is a measure of the rate of transformation of electrical energy. The unit for electric power is the watt, W. A machine that has a power rating of 1 W provides 1 joule of work per second: 1 W = 1 J/ 1 s P = E / ∆t where P is electrical power measured in watts, W E is electrical energy in joules, J ∆t is the amount of time that has passed in seconds, s

Relationship between Power and Energy It is possible to determine the quantity of energy consumed by an electrical device by multiplying its power by time: 1 W x 1s = 1 J/s x 1 s =1 J P xt=E Energy can be measured in Joules, J, but it can also be measured in kilowatt hours (kWh). 1 kWh=1000 W x 3600 s = J

Example : A 1000 W microwave is used for 6 minutes. How much energy (in Joules) will it consume? E =Pxt =1000 W x6 minutesx 60 seconds/minute = J The microwave will consume J (or 36 kJ) of energy in 6 minutes.

Power, Voltage, Current and Resistance Recall that 1V = 1 J/C; in other words if a resistor's voltage drop is 1 V, then 1 J of energy has been lost for every coulomb of charge that goes through that resistor. Also, 1 A = 1 C/s; in other words if a 1 A current goes through a light bulb, then it means that 1 C of charge is going by every second. Now let's multiply the units of V by those of I. (J/C) (C/s) = J/s. Those are the units for power! So that means: P = VI or substituting Ohm's Law P = I 2 R

Example What is the power rating of a 10 Ω resistor that operates at 120 V. P = E x t =V x I=I 2 x R I = V/R = 120 v/ 10 Ω = 12 A P = V x I = 120 V x 12 A = 1440 W The 10 Ω resistor has a power rating of 1440 W.

Relating Energy to Power Since by definition E = P x t, where if P is power in watts( J/S = W) and time is measured in seconds, then E will be in joules (J). Substituting P = VI in to the above formula: E = V x I x t

Example A heating coil has a resistance of 10 Ω. It is designed to operate at 120 V. If it is on for 200 hours, how much energy was consumed? E = V x I x t = 120 v x 12 A x 200 h x 60 minutes/hour x 60 seconds / minute = J = kJ The heating coil will consume kJ in 200 hours.