Voltage and current are two fundamental electrical circuit parameters. However, only voltage and current are not enough to express an electrical circuit element’s behaviour. Essentially, we need to understand how much electrical power a circuit element can manage. We have all seen that an electric lamp of 60 watts provides less light than an electric lamp of 100 watts. When we pay electric bill for the consumption of electricity, we effectively pay the electric power charges for a particular period of time. To analyze an electrical circuit or network, the calculation of electrical power is therefore quite crucial.
Electric Power is the rate of energy that an electrical element supplies or consumes over time.
Suppose an element supplies or consumes a dw joules energy for a period of dt second, then the element’s power can be represented as,
You can also rewrite this equation as,
Therefore the power is also instantaneous as the expression of voltage and current in the equation is instantaneous. The power that is expressed varies in time.
Thus, a circuit element’s power is the product of voltage throughout the element and the current through it.
As we already said, a circuit element can either absorb or supply power. By putting a positive sign (+) in the expression of power we represent the absorption of power. Likewise, if we represent the power supplied by the circuit element, we put a negative sign-).
Passive Sign Convention
There is a simple relationship among the direction of current, sign of the power and polarity of voltage of a circuit element. We call this easy connection a passive sign convention. When a current enters an element through its positive voltage polarity terminal, we placed a positive sign (+) before the voltage and current product. This means that the component absorbs or consumes energy from the electrical circuit. On the other side, when the current through the component leaves its terminal of favorable voltage polarity, we placed a negative sign (-) before the voltage and current product. This means that the element deliver power to the electrical circuit.
Let us connect a resistor across two circuit terminals. Although the extra part of the circuit is not shown in the figure here. The direction of current through the resistor and the polarity of the voltage drop across the resistor are shown in the figure below. S shown in fig. the resistor is consuming a power of vi watts as current i ampere enters in the resistor though its positive side of the dropped voltage v volt.
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