POWER AND ENERGY

Power and energy calculation are very important in circuit analysis. Although voltage and current are useful variables in an electric circuit, they are not sufficient by themselves. One reason is that the useful output of the system often is non-electrical, and this output is conveniently expressed in terms of power and energy. Another reason is that all practical devices have limitations on the amount of power that they can handle. For example, we all know from our experience that a 60-watt bulb gives more light than 40-watt bulb. We also know that when we pay our electricity bills, we are paying for the electrical energy (watt-hour) consumed over a certain period of time.
We now relate power and energy to voltage and current, we recall from physics that: power is the time rate of expending or absorbing energy.
Power is measured in watts(W). Mathematically we write this relationship as,
p=dw/dt..................................... (1.6)
where,
p=power in watts
w=the energy in joule
t=time in second
Thus, 1 watt=1 joule/sec
p=dw/dt=(dw/dq)*(dq/dt)=v*i.......... (1.7)
Above equation shows the power associated with a basic circuit element is simply the product of the current in the element and the voltage across the element. Therefore, power is a quantity associated with a pair of terminals, and we have to be able to tell from our calculation whether power is being delivered to the element or supplied by the element. If the power has a (+)ve sign, power is being delivered to or absorbed by the element. But,how do we know when the power has a positive or a negative sign.
Polarity of voltage and direction of current play a major role in determining the sign of power.

In order to have power a positive sign, the direction of current and polarity of voltage must Conform with those shown in figure (a). By the passive sign convention, current enters through the positive polarity of the voltage and in this case p=+vi or vi>0 implies that the element is absorbing power. But if p=-vi or vi<0, as in figure (b), the element is releasing or supplying power.
Passive sign convention is satisfied when the current enters through the positive terminal of an element and p=+vi. However, if the current enters through the negative terminal, p=-vi.
In general we can write,
+power absorbed=-power supplied.

For any electric circuit, law of conservation of energy must be obeyed. For this reason, at any instant of time, the algebraic sum of power in a circuit must be zero. Therefore, we can write,

∑p=0................ (1.8)

Equation (1.8) confirms the fact that the total power supplied to the circuit must balance the total power absorbed.
To calculate the energy w supplied or absorbed by a circuit element between time instant t0 and t, we get integrate power. Therefore,

w=∫p dt=∫v.i dt................ (1.9)

Thus,energy is the capacity to do work. Energy is measured in joules.
The electric power utility companies measure energy in watt-hour (Wh).
Where, 1 Wh=3600 joules.