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

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.