- Electric Power Definition: Electric power is the rate at which an electrical circuit or component consumes or delivers energy over time.
- Calculation Method: The formula P = dW/dt, where dW is the energy in joules and dt is the time in seconds, calculates electric power.
- Usage Examples: Understanding electric power helps in assessing the efficiency of different devices and in calculating electricity bills.
- Passive Sign Convention: This convention determines the sign of power based on the direction of current and voltage polarity, indicating consumption or delivery.
- Practical Application: Examples like a resistor consuming power and a battery delivering power demonstrate the practical implications of electric power calculations.
Voltage and current are two basic parameters of an electric circuit. But, only voltage and current are not sufficient to express the behaviour an electric circuit element. We essentially need to know, how much electric power, a circuit element can handle. All of us have seen that a 60 watts electric lamp gives less light than a 100 watts electric lamp. Our electric bills reflect the charges for the electric power consumed over a specified period. Calculating electric power is essential for analyzing electric circuit or network efficiency.
Suppose, an element supplies or consumes an energy of dw joules for a time of dt second, then power of the element can be represented as,
This equation can be expressed differently to clarify its components.
Hence, from the as the expression of voltage and current in the equation are instantaneous, the power is also instantaneous. The expressed power is time-varying.
So, the power of a circuit element is the product of voltage across the element and current through it.
As we have already told that a circuit element can either absorb or deliver power. We represent the absorption of power by putting a positive sign (+) in the expression of power. Likewise, we put a negative sign (-) when we represent the power delivered by the circuit element.
Passive Sign Convention
There is a simple relationship between the direction of current, polarity of voltage and sign of the power of a circuit element. We call this simple relationship as passive sign convention. When a current enters in an element through its terminal of positive voltage polarity, we put a positive sign (+) before the product of the voltage and current. This implies that the element absorbs or consumes power from the electric circuit. On the other hand, when the current through the element leaves its terminal of positive voltage polarity, we put a negative sign (-) before the product of the voltage and current. This implies that the element delivers or supplies power to the electric circuit.
Let us take a resistor connected across two circuit terminals. Although, the rest of the circuit is not shown here in the figure. The polarity of the voltage drop across the resistor and the direction of current through the resistor are shown in the figure below. 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, as shown.
Let us take a battery connected across two circuit terminals. Although, the rest of the circuit is not shown here in the figure. The polarity of the voltage drop across the battery and the direction of current through the battery are shown in the figure below. The battery is delivering a power of vi watts as current i ampere enters in the battery of v volt through its positive polarity terminal as shown.
