Electric Power

Introduction to Electric Power

Electric power is a measure of how quickly electrical energy is converted into another form of energy, such as heat, light, or mechanical energy, in an electrical circuit. It tells us the rate at which work is done or energy is consumed in an electric circuit. The SI unit of electric power is the watt (W), which is equivalent to one joule per second.

In simple terms, electric power indicates how much energy is used or produced by an electrical device over time. Devices like electric heaters, bulbs, and fans all consume electric power to operate, and understanding how to calculate electric power helps in determining energy consumption and efficiency.

Definition of Electric Power

Electric power () is defined as the rate at which electrical energy is consumed or generated in a circuit. Mathematically, it is given by the formula:

Where:

• = Electric power (in watts, W),
• = Voltage (in volts, )
• = Current flowing through the circuit (in amperes, ).

This formula shows that power is the product of the potential difference (voltage) across the component and the current flowing through it.

Alternate Formulas for Electric Power

 Using Ohm’s Law (), we can derive other useful formulas for calculating electric power in terms of current and resistance, or voltage and resistance:

Power in Terms of Current and Resistance:

This formula is useful when you know the current flowing through a resistor and its resistance.

Power in Terms of Voltage and Resistance:

This formula is helpful when you know the voltage across a resistor and its resistance.

Electrical Energy

Electrical energy is the total amount of energy consumed or produced in a circuit over a certain period. It is related to electric power and is given by the formula:

Where:

• = Electrical energy (in joules, ),
• = Power (in watts, ).
• = Time for which the power is consumed or produced (in seconds, ).

For practical purposes, electrical energy is often measured in kilowatt-hours (kWh), which is the unit used by electricity companies to bill customers. One kilowatt-hour is the amount of energy consumed by a 1 kW appliance running for 1 hour.

Power Ratings of Devices

Most electrical appliances are labeled with their power rating, which tells you how much power they consume when operating at their rated voltage. This information helps users understand how much electricity the device uses.

For example:

• A 60 W bulb consumes 60 watts of power when it is switched on.
• A 1000 W (1 kW) electric heater consumes 1 kW of power.

The power rating of a device helps you estimate the energy consumption over time. For example, if a 1000 W heater runs for 2 hours, the energy consumed would be:

Practical Examples of Electric Power

Let’s explore how to apply the concept of electric power with examples:

Example 1: Power Calculation

A 10 A current flows through a 240 V electric appliance. Calculate the power consumed by the appliance.

Solution:

• Given: , .
• Using the formula::

     

Thus, the appliance consumes of power.

Example 2: Energy Consumption

A 1500 W microwave oven is used for 30 minutes. Calculate the energy consumed in kilowatt-hours (kWh).

Solution:

• Given: , .
• Using the formula for electrical energy: :

     

Thus, the microwave consumes of energy.

Example 3: Power in Terms of Resistance

An electric kettle has a resistance of 20 Ω and operates with a voltage of 220 V. Calculate the power consumed by the kettle.

Solution:

• Given: , .
• Using the formula: ​:

     

Thus, the power consumed by the kettle is or .

Commercial Unit of Electrical Energy: Kilowatt-Hour (kWh)

The kilowatt-hour (kWh) is the unit used by electricity companies to measure energy consumption and calculate electricity bills. One kilowatt-hour is the energy consumed by a device with a power rating of 1 kilowatt operating for 1 hour.

To calculate the total energy consumed in kWh, use the formula:

Where:

• = Power (in watts, ),
• = Time (in seconds, ).

Electricity companies typically charge for each kWh of energy consumed. For example, if the cost per kWh is ₹6, and you use 100 kWh in a month, your electricity bill will be:

Relationship Between Power, Current, and Voltage

Electric power depends on both current and voltage in a circuit. Let’s break down the key relationships:

If Voltage Increases:

• For a given resistance, increasing the voltage will increase the current, which in turn increases the power.

If Current Increases:

• For a constant voltage, increasing the current will result in more power being consumed by the device. Power is proportional to the square of the current when resistance is constant.

Effect of Resistance:

• For a constant voltage, higher resistance results in lower current, thus reducing the power consumed.
• For a constant current, increasing the resistance increases the power consumed.

Power in Series and Parallel Circuits

Power in Series Circuits:

• In a series circuit, the current is the same through all components, but the voltage across each component is different depending on its resistance. The total power consumed is the sum of the power consumed by each resistor:

     

Power in Parallel Circuits:

• In a parallel circuit, the voltage across each component is the same, but the current differs depending on the resistance. The total power consumed is the sum of the power consumed by each branch:

     

Real-Life Applications of Electric Power

Household Appliances

• Every household appliance consumes electric power when it operates. For example, an air conditioner typically consumes between 1 to 2 kW of power, while a refrigerator consumes around 150 W.

Electric Vehicles

• Electric vehicles (EVs) rely on battery power to drive their motors. The power consumption of an EV is measured in kW, and the distance the vehicle can travel is determined by the energy stored in the battery (measured in kWh).

Power Generation

• Power plants generate electricity in megawatts (MW) to supply cities and industries. The power generated by these plants is transmitted through electrical grids and used to meet the energy demands of consumers.

Industrial Machinery

• Factories use heavy machinery that consumes significant amounts of power, typically in kilowatts or megawatts. Understanding power consumption helps industries manage energy efficiency and reduce costs.

Key Practice Questions

Q1: A 100 W light bulb operates for 10 hours. Calculate the energy consumed in kilowatt-hours.

• Answer:

     

Q2: A heater draws 5 A of current and operates at 220 V. Calculate the power consumed by the heater.

• Answer:

     

Q3: A resistor has a resistance of 50 Ω, and the voltage across it is 200 V. Calculate the power consumed by the resistor.

• Answer:

     

Q4: If the electricity cost is ₹6 per kWh, calculate the cost of running a 2 kW air conditioner for 8 hours.

• Answer:

     

     

FAQs