Electric Power Formula

electric power

Although current and voltage are fundamental variables for electric circuits, they are not still sufficient to solve all the electrical phenomenon. We still need electric power.

In fact, we still need to know how much power an electronic device can handle.

Before moving on make sure to read what is dc circuit first. And then read the linear circuit analysis.

 

Electric Power and Energy

For example, a 120-watt bulb will shine brighter than a 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 the physic statement :

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

And the mathematic equation is :

electrical power equation
(1)

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 :

electrical power equation
(2)

or

electrical power equation
(3)

The mathematic equation in Equation.(3) is called by instantaneous power. If the power has a positive (+) sign, the power is being delivered to an element or the element is absorbing power.

In opposite negative (-) sign means the power is being supplied by element. This condition can be seen in Figure.(1).

electrical power signs
Figure 7. Power signs

In order to determine the sign of power, we need to consider the current and voltage direction first.

For a convenient method of this problem, we can review the relationship between current, voltage, and power.

Please refer to Figure.(1) for better understanding of the relationship between these three parameters.

element absorbing power
Figure 2. Elemet absorbing power

Figure.(2) shows how to get a positive sign. This is known as the passive sign convention.

This convention shows how the current enters through the 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.

element delivering power
Figure 3. Elemet delivering power

Passive sign convention is achieved when the current enters through the positive terminal of an element and p = +vi, if the current enters the negative terminal, p = -vi.

For illustration above we will conclude that :

+Power absorbed = -Power supplied

because absorbing power of -12W is the same with supplying power of +12W.

We now understand that law of conservation of energy must be obeyed by any electric circuit. The mathematic equation itself may follow :

law of conservation of energy
(4)

From the equation above it makes sure that the total power absorbed must balance the total power supplied.

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

mathematic energy equation
(5)

Energy is the capacity to do work, measured in joules (J)

The electric power utility measure their energy in watt-hours (Wh) where :

1 Wh = 3.600 J

Electric Power Formula Examples

For better understanding let us review some examples below :

1. An energy source 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 :

Potential difference

2.Calculate the power delivered to an element at t = 3 ms if the current is entering at the positive terminal

i =  5 cos 60 π t A

and the voltage is : (a) v = 3i ; and (b) v = 3 di/dt

Solution :

Potential difference