1.3 : Power and Energy

The power and energy delivered to an element are subjects of great significance in the field of electrical engineering. It is a well-known fact that a 100-watt light bulb emits more light than a 60-watt one. Therefore, power and energy calculations play a crucial role in the analysis of electrical circuits.

Power, defined as the time rate of expending or absorbing energy, is quantified in units called watts (W). The relation between power and energy is mathematically given as

where "p" represents the power in watts (W), "w" denotes the energy in joules (J), and "t" signifies the time in seconds (s).

The power associated with the current passing through an element within a circuit is the product of the voltage across that element and the current flowing through it. When the current enters the circuit element at the positive terminal of the voltage and exits at the negative terminal, it adheres to the passive convention. In this convention, the voltage propels a positive charge in the same direction as indicated by the current. Consequently, the power computed by multiplying the element voltage by the element current represents the power received by the element. This power is occasionally referred to as "the power absorbed by the element" or "the power dissipated by the element." Importantly, the power received by an element can assume either positive or negative values, contingent upon the actual values of the element's voltage and current.

On the other hand, when the passive convention is not adhered to, the current enters the circuit element at the negative terminal of the voltage and exits at the positive terminal. In this case, the voltage drives a positive charge in the direction opposite to that indicated by the current. Therefore, when the element voltage and current do not comply with the passive convention, the power computed by multiplying these values represents the power supplied by the element. Similar to received power, supplied power can also be positive or negative, depending on the specific values of the element's voltage and current.

The relationship between the power received by an element and the power supplied by that same element is expressed as

When the element voltage and current align with the passive convention, the energy received by an element is given by

Energy is defined as the capacity to perform work and is expressed in joules (J).