11.8. Electric Power

You have studied in your earlier Class that the rate of doing work is power. This is also the rate of consumption of energy. Equation (11.21) gives the rate at which electric energy is dissipated or consumed in an electric circuit. This is also termed as electric power. The power P is given by P = VI Or P = I²R = V²/R (11.22)

Electric power is defined as the rate of doing work or consuming energy in an electric circuit. This means that power indicates how much energy is used over a certain period. In electrical terms, power can be calculated in three different ways based on the parameters available:

1. Using voltage and current (P = VI)
2. Using current and resistance (P = I²R)
3. Using voltage and resistance (P = V²/R) Each of these equations shows how power is related to the other fundamental quantities in electric circuits.

Think of electric power like the flow of water in a pipe. Just as the rate at which water flows through a pipe (gallons per minute) shows how much water is used over time, electric power tells us how much electrical energy is being consumed or produced. For instance, a light bulb that uses more watts is like a larger water pipe - it's capable of allowing a larger amount of water, or in this case, energy to flow through at any given time.

The SI unit of electric power is watt (W). It is the power consumed by a device that carries 1 A of current when operated at a potential difference of 1 V. Thus, 1 W = 1 volt × 1 ampere = 1 VA (11.23). The unit ‘watt’ is very small. Therefore, in actual practice we use a much larger unit called ‘kilowatt’. It is equal to 1000 watts.

The standard unit of power in an electrical context is the watt, abbreviated as 'W'. One watt equates to the amount of power that is used when one ampere of current flows through a device at a voltage of one volt. However, since a watt is a relatively small measure, we often refer to kilowatts (kW) in practical situations, where 1 kilowatt equals 1000 watts.

Imagine you are filling up a bottle of water, and you have a tiny cup that holds just 1 milliliter (1 W of power). Filling it can take a long time with just that little cup. Instead, if you switch to a larger container, like a bucket (1 kW), you can fill the bottle much faster! In electrical terms, using kilowatts makes it easier and more practical to describe the power needs of larger appliances, like refrigerators and air conditioners.

Since electrical energy is the product of power and time, the unit of electric energy is therefore watt hour (W h). One watt hour is the energy consumed when 1 watt of power is used for 1 hour. The commercial unit of electric energy is kilowatt hour (kW h), commonly known as ‘unit’. 1 kW h = 1000 watt × 3600 second = 3.6 × 10^6 watt second = 3.6 × 10^6 joule (J)

Electric energy consumption is calculated by multiplying the power (in watts) by the time the power is consumed (in hours). This results in watt-hours (Wh), which is a measure of energy used. A more common measurement for larger appliances is kilowatt-hour (kWh), helping us determine how much energy an appliance uses over time in a more manageable figure. For example, if a device uses 1000 watts (1 kW) for one hour, it consumes 1 kWh.

Imagine you have a battery-powered toy. If you play with it using a battery that powers the toy at 10 watts for 5 hours, you have used 50 watt-hours of energy (10 W x 5 h). This concept is similar to filling a bucket with water - the more gallons you pour each minute (power), over how long you pour (time), gives you a total volume of water (energy consumed).

An electric bulb is connected to a 220 V generator. The current is 0.50 A. What is the power of the bulb? Solution: P = VI = 220 V × 0.50 A = 110 J/s = 110 W.

To find the power consumed by an electric bulb, we can use the formula P = VI, where V is voltage and I is current. By substituting the given values (V = 220 V and I = 0.50 A) into the equation, we determine the power to be 110 watts. This value represents the energy the bulb uses per second.

Think of a kettle that boils water. If you know the kettle uses 2200 watts (2.2 kW) of power, you can see how quickly it heats up water. Like the bulb using energy constantly, the kettle does too, but since it uses more wattage, it boils water faster. Power usage directly relates to the energy consumed to perform a task.

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