Electrical Energy And Power - Battery

Electrical Energy and Power - Battery

Definition of electrical energy
Importance of electrical energy
Concept of power
Calculation of electrical power
Units of electrical energy and power

Definition of Electrical Energy

Electrical energy is the work done by an electric circuit or device per unit time.
It is the product of power and time.

Importance of Electrical Energy

Electrical energy is essential for providing power to various devices and systems.
It is used for lighting, heating, cooling, transportation, communication, etc.

Concept of Power

Power is the rate at which work is done or energy is transferred.
It is defined as the work done or energy transferred per unit time.
Power is measured in watts (W).

Calculation of Electrical Power

Power (P) = Work (W) / Time (t)
P = V * I, where V is the voltage and I is the current

Units of Electrical Energy and Power

The unit of electrical energy is the kilowatt-hour (kWh).
1 kWh is equal to 3.6 × 10^6 joules (J).
The unit of electrical power is the watt (W).

Examples of Electrical Energy and Power

An electric bulb rated at 100 W is switched on for 5 hours. Calculate the electrical energy consumed.
Solution: Energy (E) = Power (P) × Time (t)
- E = 100 W × 5 hours = 500 Wh = 0.5 kWh

Calculation of Electrical Power

The power consumed by an electrical device can be calculated using the formula:
- Power = Voltage × Current

Example:

A device has a voltage of 12 V and a current of 2 A. Calculate the power consumed by the device.
Power = 12 V × 2 A = 24 W

Relationship Between Energy and Power

Electrical energy is directly proportional to the power and the time for which the device is used.
The greater the power and the longer the time, the more electrical energy is consumed.

Example:

A power drill consumes 500 W of power and is used for 2 hours. Calculate the electrical energy consumed.
Energy = Power × Time
Energy = 500 W × 2 hours = 1000 Wh = 1 kWh

Electrical Energy and Cost Calculation

To determine the cost of electrical energy consumed, we need to know the rate per unit of electrical energy, usually given in ₹/kWh.

Example:

If the cost of electricity is ₹5 per kWh, calculate the cost of using a 1000 W appliance for 6 hours.
Energy = Power × Time
Energy = 1000 W × 6 hours = 6000 Wh = 6 kWh
Cost = Energy × Cost per kWh
Cost = 6 kWh × ₹5/kWh = ₹30

Efficiency of Electrical Devices

Efficiency is a measure of how effectively a device converts electrical energy into useful work.
It is expressed as a percentage.
Efficiency = (Useful Energy Output / Total Energy Input) × 100

Example:

A light bulb converts 20% of the electrical energy into light. Calculate the efficiency of the light bulb.
Efficiency = (Useful Energy Output / Total Energy Input) × 100
Efficiency = 20%

Relationship Between Power and Current

Power in an electrical circuit can also be calculated using the formula:
- Power = Current^2 × Resistance

Example:

A circuit has a current of 2 A flowing through it and a resistance of 4 ohms. Calculate the power dissipated in the circuit.
Power = Current^2 × Resistance
Power = 2 A^2 × 4 Ω = 16 W

Electric Circuit Components

Voltage source
Electrical conductors
Resistors
Capacitors
Inductors

Voltage Source

Provides the electrical energy necessary for the circuit to operate.
Common types of voltage sources: batteries, generators, and power supplies.

Electrical Conductors

Allow the flow of electric current.
Examples: copper wires, aluminum wires.

Resistors

Components that resist the flow of electric current.
Oppose the flow of electric charge.
Used to control the amount of current flowing through a circuit.
Symbol: $ R $
Measured in Ohms ( $ \Omega $ )

Capacitors

Store electrical energy in the form of electric charge.
Consist of two conductive plates separated by an insulating material.
Symbol: $ C $
Measured in Farads ( $ F $ )

Inductors

Components that store electrical energy in the form of a magnetic field.
Consist of a coil of wire.
Symbol: $ L $
Measured in Henrys ( $ H $ )

Examples:

A circuit contains a 2 ohm resistor and a 4 farad capacitor. Calculate the total impedance of the circuit.
Impedance ( $ Z $ ) = $ \sqrt{R^2 + \left(\frac{1}{\omega C}\right)^2} $

Ohm’s Law

States the relationship between voltage, current, and resistance in an electrical circuit.
$ V = IR $
$ I = \frac{V}{R} $
$ R = \frac{V}{I} $

Example:

A circuit has a voltage of 12 V and a resistance of 3 ohms. Calculate the current flowing through the circuit.
$ I = \frac{V}{R} = \frac{12V}{3\Omega} = 4A $

Kirchhoff’s Laws

Kirchhoff’s First Law (KCL)

The sum of currents entering a junction in a circuit is equal to the sum of currents leaving the junction.
Conservation of charge.

Kirchhoff’s Second Law (KVL)

The sum of voltage drops around any closed loop in a circuit is equal to the sum of all voltage rises.
Conservation of energy.

Series Circuits

Components are connected end to end.
Current remains the same through all components.
Voltage drops across each component add up to the total voltage.
Equivalent resistance ( $ R_{eq} $ ) of series resistors: $ R_{eq} = R_1 + R_2 + R_3 + … $

Example:

A series circuit has three resistors with values 5 ohms, 3 ohms, and 2 ohms. Calculate the total resistance of the circuit.
$ R_{eq} = 5\Omega + 3\Omega + 2\Omega = 10\Omega $

Parallel Circuits

Components are connected across each other.
Voltage across each component is the same.
Current divides among the different branches.
Equivalent resistance ( $ R_{eq} $ ) of parallel resistors: $ \frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + … $

Example:

A parallel circuit has three resistors with values 10 ohms, 5 ohms, and 2 ohms. Calculate the total resistance of the circuit.
$ \frac{1}{R_{eq}} = \frac{1}{10\Omega} + \frac{1}{5\Omega} + \frac{1}{2\Omega} \Rightarrow \frac{1}{R_{eq}} = \frac{1}{2\Omega} $

Power in Circuits

Power ( $ P $ ) is the rate at which energy is transferred in a circuit.
Power can be calculated using the formulas:
- $ P = IV $
- $ P = I^2R $
- $ P = \frac{V^2}{R} $

Example:

A circuit has a current of 5 A and a voltage of 10 V. Calculate the power dissipated in the circuit if the resistance is 2 ohms.
$ P = IV = 5A \times 10V = 50W $

Energy in Circuits

Electrical energy ( $ E $ ) can be calculated using the formula:
- $ E = Pt $
Energy is measured in joules ( $ J $ ).
1 kilowatt-hour ( $ kWh $ ) = 3600 kilojoules ( $ kJ $ ).

Example:

A device is rated at 1000 W and is used for 2 hours. Calculate the electrical energy consumed.
$ E = Pt = 1000W \times 2h = 2000Wh = 2kWh $

Electric Circuits and their Components

Resistors: Components that resist the flow of electric current.
Capacitors: Components that store electrical energy in the form of electric charge.
Inductors: Components that store electrical energy in the form of a magnetic field.
Voltage sources: Provide electrical energy to the circuit.
Conductors: Allow the flow of electric current.

Ohm’s Law

Ohm’s Law states that the current flowing through a conductor between two points is directly proportional to the voltage across the two points, and inversely proportional to the resistance of the conductor.
Mathematically, it can be represented as: $ V = I \times R $ , where $ V $ is voltage, $ I $ is current, and $ R $ is resistance.
Ohm’s Law is widely used to analyze and design electrical circuits.

Kirchhoff’s Laws

Kirchhoff’s First Law (KCL): The algebraic sum of currents at any junction in a circuit is zero.
Kirchhoff’s Second Law (KVL): The sum of the electromotive forces (emfs) and potential drops in any closed loop in a circuit is zero.

Series Circuits

Components are connected in a series, i.e., end to end.
The same current flows through each component.
The total resistance ( $ R_{total} $ ) is equal to the sum of individual resistances ( $ R_1, R_2, R_3, … $ ). $ R_{total} = R_1 + R_2 + R_3 + … $
The voltage across each component is proportional to its resistance.

Parallel Circuits

Components are connected in parallel, i.e., across each other.
The voltage across each component is the same.
The total resistance ( $ R_{total} $ ) is calculated using the formula: $ \frac{1}{R_{total}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + … $
The current is divided among the different branches based on their resistances.

Power in Electric Circuits

Power ( $ P $ ) in an electric circuit is the rate at which electrical energy is converted into other forms of energy, such as heat or light.
Power can be calculated using the formulas:
- $ P = I \times V $
- $ P = I^2 \times R $
- $ P = \frac{V^2}{R} $
Power is measured in watts ( $ W $ ).

Energy in Electric Circuits

Electrical energy ( $ E $ ) is the amount of work done by an electric circuit over a period of time.
Electrical energy can be calculated using the formula: $ E = P \times t $ , where $ P $ is power and $ t $ is time.
The unit of electrical energy is the joule ( $ J $ ).

Efficiency of Electric Circuits

Efficiency is a measure of how effectively an electric circuit converts electrical energy into other forms of energy.
It is calculated using the formula: $ Efficiency = \frac{\text{Useful output energy or power}}{\text{Total input energy or power}} \times 100% $
Efficiency is expressed as a percentage.

Calculation of Efficiency

Example 1: A device consumes 1000 J of electrical energy and produces 800 J of useful work. Calculate the efficiency.
- Efficiency = $ \frac{800 \text{ J}}{1000 \text{ J}} \times 100% = 80% $
Example 2: A motor consumes 500 W of electrical power and produces 450 W of useful work. Calculate the efficiency.
- Efficiency = $ \frac{450 \text{ W}}{500 \text{ W}} \times 100% = 90% $

Application of Electrical Energy and Power in Daily Life

Usage of electrical energy and power in lighting homes, offices, streets, etc.
Appliances such as refrigerators, air conditioners, televisions, etc., rely on electrical energy.
Electrical power is used in industries for various processes and machinery.
Transportation systems, including electric cars and trains, utilize electrical energy for operation.