## Electrical Power and Energy

Although current and voltage are fundamental variables for electric circuits, they are not still sufficient to solve all the electrical phenomenon. In fact we still need to know how much

*power*an electronic devices can handle. For example, 120-watt bulb will shine brighter than 60-watt bulb. Another easy example is electricity bills that we pay is based on how much electric energy we used in a certain period of time. Hence, the analysis of power and energy are taking important part besides current and voltage in circuit analysis.
To discover the relationship between energy and power to current and voltage, we have physic statement :

Power is the time rate of expending or absorbing energy, measured in watts (W)

where :

*p*= power (watts = W)

*w*= energy (joules = J)

*t*= times (seconds = s)

Combining the Equation.(1) with the equation of voltage and equation of current results :

or

Mathematic equation in Equation.(3) is called by

*instantaneous power*. If the power has positive (+) sign, the power is being delivered to element or the element is absorbing power. In opposite negative (-) sign means the power is being supplied by element. These condition can be seen in Figure.(1).

Figure 7. Power signs |

Figure 2. Elemet absorbing power |

*passive sign convention*. This convention shows how the current enters through positive polarity of voltage, makes

*p*= +

*vi*or

*p*> 0 implies that the element is absorbing power. In opposite for

*p*= -

*vi*or

*vi*< 0 in Figure.(3) means the element is delivering or supplying power.

Figure 3. Elemet delivering power |

For ilustration above we will conclude that :Passive sign conventionis achieved when the current enters through the positive terminal of an element andp = +vi, if the current enters the negative terminal,p = -vi.

**+Power absorbed = -Power supplied**

We now understand that

*law of conservation of energy*must be obeyed by any electric circuit. The mathematic equation itself may follow :

(4) |

Using Equation.(2) but in changing condition in a spesific period of time, the equation transforms into :

(5) |

The electric power utility measure their energy in watt-hours (Wh) where :Energyis the capacity to do work, measured in joules (J)

**1 Wh = 3.600 J**

For better understanding let us review some examples below :

**1.An energy sources forces a constant current of 2 A for 10 s to flow to a light bulb. If 2.3 kJ is used as light and heat energy, how much voltage drop for the bulb?**

__Solution :__**2.Calculate the power delivered to an element at**

*t*= 3 ms if the current is entering at positive terminal

*i*= 5 cos 60*π t*A**and the voltage is : (a)**

*v*= 3*i*; and (b)*v*= 3*di/dt*

__Solution :__
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