﻿ Electricity Notes | Science Olympiad Class 10

# Electricity

## Electricity - Class 10 Science

• Electricity
• Electric Charges
• Electric Potential
• Electric Current
• Electric Circuit
• Ohm's Law
• Resistance of a Conductor
• Conductors, Insulators and Resistors
• Resistivity
• Combination of Resistance
• Domestic Electric Circuits: Series or Parallel
• Electric Power
• Electrical Energy
• Heating Effect of Current
• Solved Questions on Electricity
• ## Electricity

Electricity is a fundamental and versatile form of energy that is essential in our modern world. It is a phenomenon resulting from the movement of electric charges, primarily electrons, through conductive materials like wires and circuits. Electricity plays a crucial role in various aspects of our lives, from powering our homes and electronic devices to driving industrial processes and transportation systems.

## Electric Charges

Electric charges are fundamental properties of subatomic particles, such as electrons and protons, that play a central role in the behaviour of matter and the interactions between objects.

Types of Charges: Electric charges come in two fundamental types:

1. Protons: These are positively charged particles found in the nucleus of atoms. A proton carries a positive charge of approximately 1.6 × 10−19 coulombs.
2. Electrons: These are negatively charged particles that orbit the nucleus of atoms. An electron possesses a negative charge of approximately 1.6 × 10−19 coulombs.

Charge Conservation: According to the law of conservation of charge, the total electric charge in a closed system remains constant. This means that charges cannot be created or destroyed; they can only be transferred between objects.

Charge Transfer: Objects can acquire electric charges through various processes, such as:

1. Friction: When two objects rub against each other, electrons can be transferred from one object to the other, resulting in one object becoming negatively charged and the other positively charged.
2. Conduction: Electric charges can flow from one object to another when they are in direct contact.
3. Induction: The rearrangement of charges within an object due to the presence of a nearby charged object can induce an opposite charge on one side of the object.

Opposite Charges Attract, Like Charges Repel: One of the fundamental principles of electric charges is that opposite charges attract each other, while like charges repel each other.

For example:

• A positive charge (+) attracts a negative charge (–).
• A positive charge (+) repels another positive charge (+).
• A negative charge (–) repels another negative charge (–).

SI Unit: The standard unit of electric charge is the coulomb (C). One coulomb is defined as the charge that passes through a conductor when a current of one ampere (1 A) flows for one second (1 s).

Quantisation of Electric Charge: The principle of quantisation of electric charge states that the total charge acquired by a body is always a whole-number multiple of the magnitude of the charge on a single electron. Mathematically, this principle can be expressed as:

q = n x e

Where:
q represents the total electric charge acquired by a body.
n is an integer that represents the number of elementary charges (electrons or protons) gained or lost.
e is the charge of a single electron, approximately equal to 1.6 × 10−19

This principle reflects the fundamental nature of electric charge, indicating that charge comes in discrete units or quanta, and it cannot exist as a fraction of the charge of an electron.

## Electric Potential

Electric potential represents the electric energy associated with a point in an electric field.
When a small positive test charge is placed in the electric field generated by another charge, it experiences a force due to the electric field. To move this test charge against the force of repulsion (or attraction, depending on the charges involved), work must be done on the charge.
The electric potential at a specific point in an electric field is defined as the amount of work done in moving a unit positive charge from infinity (where there is no influence from the field) to that point.

Unit: The unit of electric potential is the volt (V). Specifically, 1 volt at a point signifies that 1 joule of work is done to transport 1 unit of positive charge (1 coulomb) from an infinite distance to that point.

### Potential Difference

Potential difference, often referred to as "voltage," is a crucial concept in electricity that describes the difference in electric potential between two points in an electric circuit.

The potential difference between two points in an electric circuit is defined as the amount of work (in joules) needed to move one unit charge (usually one coulomb) from one point to the other.

1. Unit of Measurement: The SI unit of potential difference is the volt (V). One volt is equivalent to one joule of work done per coulomb of charge moved.
2. Voltmeter: Potential difference is typically measured using an instrument called a voltmeter. The voltmeter is connected in parallel across the two points where the potential difference needs to be measured. It displays the voltage in volts.
3. Resistance: Voltmeters are designed with high resistance to ensure that they draw negligible current from the circuit they are measuring. This is because the presence of a low-resistance path could alter the potential difference being measured.
4. Voltage: The term "voltage" is often used interchangeably with a potential difference. When we talk about the voltage across a component in an electric circuit, we are referring to the potential difference between its two ends.

## Electric Current

Electric current is the flow of electric charges, specifically electrons, within a conductor. It occurs when there is a potential difference (voltage) between two points in a circuit, causing electrons to move from a region of higher potential (voltage) to one of lower potential. The flow of charges constitutes an electric current.

1. Magnitude: The magnitude of electric current (I) is defined as the amount of electric charge (Q) passing through a specific point in a conductor in one second. Mathematically, it is expressed as:
2. Unit of Measurement: The standard unit of electric current in the International System of Units (SI) is the ampere (A). One ampere is equivalent to one coulomb of charge passing through a conductor in one second.
3. Subunits: Smaller units of current are also used, including milliampere (mA) and microampere (µA), especially when dealing with small currents:
4. Measurement: Electric current is measured using an instrument called an ammeter. The ammeter is connected in series within the circuit in which the current is to be measured. It should ideally have a very low resistance to avoid altering the current being measured.

### Continuous Flow of Electric Current

1. To maintain a continuous flow of electric current, you need a potential difference (voltage) between two points in a conductor created by a cell or battery. This potential difference drives the flow of electrons, which constitute the electric current, through a conductor like a wire.
2. The simplest and most common way to create a potential difference in a circuit is by connecting a conductor (e.g., a wire) between the terminals of a cell or a battery. Inside the cell or battery, chemical reactions generate a potential difference between the positive (+) and negative (-) terminals. This potential difference acts as the driving force for the electric current.
3. For example, a single dry cell typically has a potential difference of 1.5 volts between its terminals. When you connect a conductor (e.g., a copper wire) between the cell's terminals and include a device like a bulb in the circuit, the potential difference causes electric current to flow through the wire and the bulb. This flow of current lights up the bulb, converting electrical energy into light.
4. It's important to note that the potential difference created by the cell or battery is maintained due to the chemical reactions happening inside it. As long as these reactions continue, the cell can provide the necessary potential difference to drive the current in the circuit.

### Direction of Electric Current

1. The conventional direction of electric current is considered to be from the positive terminal of a cell or battery to the negative terminal, through the outer circuit. In circuit diagrams, arrows are often used to indicate this direction.
2. In reality, electric current is the flow of electrons, which are negatively charged. Electrons flow from the negative terminal to the positive terminal of a cell or battery, which is opposite to the conventional current direction.

### Flow of Electrons

1. When a source of electricity (such as a cell or battery) is connected to a metal wire, the electric force generated by the potential difference acts on the free electrons within the wire. These electrons, being negatively charged, start moving from the negative terminal toward the positive terminal of the source. This flow of electrons constitutes the electric current in the wire.
2. In the absence of an electric field (created by a potential difference), electrons in a metal wire move randomly in all directions between the atoms of the wire.

## Electric Circuit

An electric circuit is a complete conducting path that allows electrons to move, creating an electric current.

1. Components of a Circuit: An electric circuit consists of various components, including a cell or battery, connecting wires (conductors), resistances (such as bulbs), and switches. These components are arranged in a way that forms a continuous path for the flow of electric current.
2. Cell or Battery: The cell or battery serves as the energy source in the circuit. It generates a potential difference (voltage) between its terminals, which creates the electric field necessary for the flow of electrons.
3. Conducting Path: Conducting wires, typically made of materials like copper, serve as the pathways through which electrons can move. These wires connect the various components of the circuit.
4. Switch: A switch is a device that can open or close the circuit. When the switch is closed (on), it completes the circuit, allowing electrons to flow and creating an electric current. When the switch is open (off), it breaks the circuit, preventing the flow of electrons and interrupting the current.
5. Electric Current: Electric current is the flow of electrons in the conducting path of the circuit. It is the movement of negatively charged electrons from the negative terminal of the cell (or battery) to the positive terminal.
6. Bulb as a Resistance: Components like electric bulbs act as resistances in the circuit. When current flows through a bulb, it encounters resistance, which causes the bulb to emit light and produce heat.
7. Completing the Circuit: To have a functioning circuit, it is essential to complete the conducting path. This means connecting the positive terminal of the cell to one end of the bulb (through a switch) and connecting the negative terminal of the cell to the other end of the bulb. When this connection is made, the circuit is closed and current can flow.
8. Opening the Circuit: When the switch is opened, it creates a gap in the conducting path, disconnecting one end of the bulb from the cell. This interruption in the path breaks the circuit, preventing the flow of current. As a result, the bulb goes off.
9. Controlling Current: Switches are crucial for controlling the flow of current in a circuit. They allow you to turn devices on or off, providing convenience and safety.

### Circuit Symbols

In electric circuits, symbols are used to represent various electrical components to simplify the process of drawing circuit diagrams. These symbols are known as electrical or circuit symbols. Here are some common electrical symbols and their meanings:

1. Cell: The symbol for a single cell consists of two parallel vertical lines, one long and thin (representing the positive terminal marked as "+") and one short and thick (representing the negative terminal marked as "–"). The battery symbol represents multiple cells connected in series.
2. Resistor: The resistor symbol represents a fixed resistance in the circuit. It is a zigzag line.
3. Variable Resistance (Rheostat): Variable resistance, also known as a rheostat, has two symbols. One represents a variable resistor with a sliding contact, and the other represents a variable resistor without a sliding contact.
4. Ammeter: An ammeter measures electric current in the circuit. It is represented by the letter "A" with an arrow indicating the direction of current flow. The ammeter is connected in series with the circuit.
5. Voltmeter: A voltmeter measures voltage (potential difference) in the circuit. It is represented by the letter "V" with a curved line. The voltmeter is connected in parallel with the component across which you want to measure voltage.
6. Connecting Wires: Connecting wires are represented by lines connecting various components in the circuit.
7. Switch (Plug Key): The switch symbol represents a device used to make or break an electric circuit. When open, it breaks the circuit (no current flows), and when closed, it completes the circuit (current flows).

These symbols are essential for drawing circuit diagrams accurately.

## Ohm’s Law

Ohm's Law is a fundamental principle in physics that describes the relationship between current (I), potential difference or voltage (V), and resistance (R) in an electrical circuit. It states that, at a constant temperature, the current flowing through a conductor is directly proportional to the potential difference across its ends. This can be mathematically expressed as:

Here, R represents the resistance of the conductor in ohms (Ω), and it is a constant that depends on the nature, length, area of cross-section, and temperature of the conductor.

V represents the potential difference (voltage) across the conductor's ends in volts (V).
I represent the electric current flowing through the conductor in amperes (A).

Key Points to Understand About Ohm's Law:

1. Direct Proportionality: According to Ohm's Law, the current through a conductor is directly proportional to the potential difference (voltage) applied across its ends. This means that as the voltage increases, the current also increases, and vice versa, as long as the temperature remains constant.
2. Resistance: The constant R in Ohm's Law represents the resistance of the conductor. Resistance is a property of the conductor itself and depends on factors like its material, length, cross-sectional area, and temperature. It is measured in ohms (Ω).
3. Inverse Proportionality: Ohm's Law also implies an inverse relationship between current and resistance. If the resistance increases, the current decreases, and if the resistance decreases, the current increases, provided the voltage remains constant.
4. Applications: Ohm's Law is widely used in circuit analysis and design. It allows engineers and electricians to calculate and predict the behaviour of electrical circuits.
5. Temperature Dependence: Ohm's Law assumes that temperature remains constant. In reality, the resistance of most conductors changes with temperature. This effect is known as the temperature coefficient.

## Resistance of a Conductor

1. Nature of Resistance: When electric current flows through a conductor, the electrons within it collide with each other and with the atoms and ions present in the conductor. These collisions create an obstruction or opposition to the flow of electrons, and this property of a conductor is termed "resistance."
2. Mathematical Expression of Resistance: The resistance of a conductor (R) is numerically equal to the ratio of the potential difference (V) across its ends to the current (I) flowing through it, which can be expressed as:
3. Unit of Resistance: The standard unit of resistance is the ohm (symbol: Ω). Ohm is defined as the resistance of a conductor through which a current of 1 ampere (A) flows when a potential difference of 1 volt (V) is applied across its ends. This relationship is expressed as:

## Conductors, Insulators and Resistors

Substances are categorised into three groups based on their electrical resistance: good conductors, resistors, and insulators.

### Good Conductors

1. These are substances that have very low electrical resistance. Good conductors allow electricity to flow through them easily. In other words, they facilitate the movement of electricity.
2. Examples of conductors include metals like silver, copper, and aluminium, as well as metal alloys like nichrome and manganin (used in heating elements). Carbon, specifically in the form of graphite, is also a conductor. The human body is a reasonably good conductor.
3. Conductors have loosely held electrons, known as "free electrons," that can move freely within the material. These free electrons enable the flow of electric charges, making the substance a conductor.

### Insulators

1. Insulators have extremely high electrical resistance, practically preventing the flow of electricity. They hinder the movement of electric charges.
2. Examples of insulators include glass, ebonite, rubber, most plastics, paper, dry wood, cotton, mica, bakelite, porcelain, and dry air. In the case of charged insulators, like glass or ebonite, electric charges remain bound to them and do not move away. Electricians often use rubber gloves when working with electricity to protect themselves from electric shocks, as rubber is an excellent insulator.
3. Insulators have electrons that are strongly bound to the nuclei of their atoms. There are no free electrons in insulators to facilitate the flow of electric charges.

### Resistors

1. Resistors are substances with comparatively high electrical resistance. Alloys like nichrome, manganin, and constantan (eureka) are examples of materials with high resistance.
2. Resistors are used in electrical devices where controlling or limiting the current is required. They reduce the current flowing in a circuit, which is essential for various applications.

Factors Affecting Resistance of a Conductor:

The resistance of a conductor is a property that opposes the flow of electric current through it. It depends on several factors:

1. Length: Resistance is directly proportional to the length of the conductor. In other words, as the length of a wire increases, its resistance also increases. This relationship can be understood as follows: A longer wire provides more "path" for electrons to travel through, and therefore, there are more collisions between electrons and atoms or ions in the wire, leading to increased resistance. Conversely, a shorter wire offers less resistance because there are fewer collisions. This relationship is expressed by the formula:
2. Cross-Sectional Area: Resistance is inversely proportional to the cross-sectional area of the conductor. When the cross-sectional area of a wire increases, its resistance decreases, and when the cross-sectional area decreases, resistance increases. This is because a larger area allows more electrons to flow in parallel, reducing the chances of collisions and resulting in lower resistance. Conversely, a smaller area restricts electron flow, increasing resistance. This relationship is expressed by the formula:
3. Material: Different materials have varying levels of electrical resistance. For instance, metals like copper and aluminium have low resistance, making them good conductors. In contrast, materials like nichrome, manganin, and constantan have higher resistance and are often used in resistors. The resistance of a conductor is closely tied to the number of free electrons available for electrical conduction. Materials with more free electrons have lower resistance because electrons can move more freely through them.
4. Temperature: The effect of temperature on the resistance of materials is an important phenomenon in electrical conductivity.
5. Pure Metals: For most pure metals, as temperature increases, their electrical resistance also increases. This is due to increased atomic vibrations at higher temperatures, which disrupt the flow of electrons through the metal lattice, leading to higher resistance.
6. Alloys: Certain alloys, like Manganin, Constantan, and Nichrome, are engineered to have minimal changes in resistance with temperature. Their resistance remains stable or may even decrease slightly as the temperature rises due to a balance of factors within their atomic structure.
7. Semiconductors: Semiconductors, such as silicon and germanium, exhibit a negative temperature coefficient of resistance. This means that their resistance decreases as temperature increases because higher temperatures provide more energy to electrons, allowing them to move more easily through the material.

## Resistivity

Resistivity (ρ), also known as specific resistance, is a fundamental property of materials that characterises their ability to resist the flow of electric current.

Mathematical Formulation of Resistivity:

Resistance of a conductor is directly proportional to its length:

Resistance of a conductor is inversely proportional to its cross-sectional area:

By combining the relations for length and area dependence, we get:

Rearranging the equation:

Where,

R is the opposition offered by a conductor to the flow of electric current. It is measured in ohms (Ω).

ρ (rho) represents a constant called the "resistivity" of the material within the conductor. This property is sometimes referred to as "specific resistance." Resistivity is unique to each material and remains relatively constant under normal conditions.

l is the physical length of the conductor through which current flows. It is measured in metres (m).

A is the area perpendicular to the direction of current flow. It is measured in square metres (m2).

Unit of Resistivity:

The SI unit of resistivity is the ohm-metre (Ω·m), often written as ρ = Ω·m.
This unit is derived by substituting the units of resistance (ohms), cross-sectional area (square metres), and length (metres) into the formula.

Materials and Their Resistivities:

1. Different materials have different resistivities, reflecting their ability to conduct electricity.
2. Conductors like copper, silver, and aluminium have low resistivities, making them excellent conductors.
3. Alloys like nichrome are used for heating elements because they have higher resistivities.
4. Insulators like glass and diamond have very high resistivities and do not conduct electricity.
5. Semiconductors like silicon and germanium have resistivities between those of conductors and insulators and exhibit unique electrical properties.

Temperature Dependency:

1. The resistivity of most conductors, including metals, increases with temperature due to increased atomic vibrations.
2. Insulators, on the other hand, have high resistivity that remains relatively constant with temperature.
3. Semiconductors have resistivities that change significantly with temperature and other factors, making them valuable for various applications like transistors and solar cells.

The Significance of Resistivity:

1. Material Property: Resistivity is a characteristic property of materials. It quantifies how well a material conducts or resists electrical current. Materials with low resistivity are good conductors, while those with high resistivity are insulators.
2. Comparing Materials: Resistivity allows us to compare the electrical properties of different materials. For example, it helps us understand why copper and aluminium, which have low resistivity, are commonly used as conductors in electrical wiring.
3. Design and Engineering: Engineers and designers use resistivity values to select appropriate materials for electrical components and circuits. For instance, when designing heating elements, they choose materials with higher resistivity, like nichrome, to produce heat efficiently.
4. Temperature Effects: Resistivity provides insights into how a material's electrical properties change with temperature. For many materials, resistivity increases with temperature, which is a crucial consideration in electronic devices.
5. Materials Science: Resistivity is a fundamental property studied in materials science, helping researchers understand the behaviour of materials under various conditions and in different applications.
 Explore about Magnetic Effects of Electric Current

## Combination of Resistance (or Resistors)

In electrical circuits, the current flowing through a circuit is not only influenced by the potential difference (voltage) but also by the resistance present in the circuit. To achieve the desired current in circuits used in devices like radios, televisions, and similar appliances, it's often necessary to combine multiple resistances. These combinations can be made in two primary ways: (i) in series, or (ii) in parallel.

### Resistances (or Resistors) in Series

When you connect resistors in series, it means that they are arranged one after the other along the same path for the electric current to flow through.

1. Total Resistance: When resistors are connected in series, the total resistance of the combination is equal to the sum of the individual resistances.
2. Mathematically, for n resistors connected in series:

This concept can be used to calculate the equivalent resistance of any number of resistors in series.
3. Current: The same current flows through all the resistors in series. This is a fundamental property of series circuits. The total current entering one end of the series combination is equal to the total current exiting from the other end.
4. Voltage: When resistors are in series, the total voltage across the series combination is equal to the sum of the voltages across each individual resistor. In other words, the voltage is divided among the resistors proportionally to their resistance values. The higher the resistance of a resistor, the greater the voltage drop across it.
5. Resistance Summation: In a series arrangement, the current flows through one resistor before passing through the next.
This arrangement leads to an increase in the total resistance in the circuit.
As a result, the current in a series circuit is the same through all resistors, but the total resistance is the sum of the individual resistances.
6. Applications: Series combinations of resistors are commonly used in various electronic circuits for different purposes, such as voltage division and current limiting. Series resistors are commonly used for circuit protection. For example, fuses and current-limiting resistors in LED circuits are placed in series to control current and prevent damage to the components.

### Resistances (or Resistors) in Parallel

When two or more resistances are connected between the same two points, they are said to be connected in parallel because they form parallel paths for the current to flow.

1. Total Resistance: When resistors are connected in parallel, the total resistance of the combination is calculated differently than in series. In parallel, the reciprocal of the combined resistance is equal to the sum of the reciprocals of all the individual resistances.
2. Mathematically, for n resistors connected in parallel total resistance is:

This formula can be used to calculate the equivalent resistance of any number of resistors in parallel.
3. Current: In a parallel arrangement, the current can choose different paths, and it doesn't necessarily flow through all resistors. This arrangement leads to a decrease in the total resistance in the circuit compared to individual resistances. The current through each resistor may differ based on the resistance values. The resistor with lower resistance will have a higher current passing through it. In a parallel configuration, each resistor receives the full voltage supplied to the circuit and the current divides among the resistors. This means that the voltage across each resistor is the same.
4. Voltage: When resistors are connected in parallel, they share the same voltage across their terminals. This is a fundamental characteristic of parallel circuits. The voltage across each resistor is equal to the voltage applied to the entire parallel arrangement
5. Applications: Parallel combinations of resistors are often used in circuits to provide multiple pathways for current flow, voltage regulation, and current division.
They are commonly used in electronics, electrical devices, and wiring in buildings.

## Domestic Electric Circuits: Series or Parallel

When designing electric circuits for domestic purposes, it's important to choose between series and parallel configurations based on the specific needs of the application.

### 1. Series Circuits for Decorative Lighting

Series circuits are suitable for decorative lighting, such as stringing hundreds or thousands of electric bulbs.

Advantages of Series Circuits for Domestic Wiring:

1. In a series circuit, all bulbs are controlled by a single switch, making it convenient to turn them on or off simultaneously.
2. Series circuits tend to have lower currents, which can be safer in certain situations.

Disadvantages of Series Circuits for Domestic Wiring:

1. Failure of One Appliance Affects All: If one electrical appliance fails or gets damaged in a series circuit, it can disrupt the entire circuit. For example, if one bulb in a series connection blows out, all bulbs go off.
2. Limited Control: In series circuits, all appliances share a single switch, so they cannot be operated independently. Turning off one appliance would turn off all connected appliances.
3. Voltage Drop: Series circuits result in a voltage drop across appliances, which can cause them to operate dimly, affecting their performance.
4. Current Limitations: Due to increased resistance in a series circuit, it may not provide sufficient current for high-power appliances.

### 2. Parallel Circuits for Domestic Wiring

Parallel circuits are widely used in domestic wiring for lighting, appliances, and outlets.

Advantages of Parallel Circuits for Domestic Wiring:

1. Independent Operation: Each electrical appliance has its own switch, allowing independent control. For example, in a house, each bulb has its own switch.
2. Redundancy: If one appliance fails in a parallel circuit, it doesn't affect others. For instance, if one bulb burns out, the rest remain lit.
3. Consistent Voltage: Appliances in parallel circuits receive the same voltage as the power supply, ensuring proper operation.
4. Higher Current: Parallel circuits offer higher current capacity, suitable for powering various appliances, including high-power devices like electric irons and water heaters.

Disadvantages of Parallel Circuits for Domestic Wiring:

1. Electrical Overloads: While parallel circuits offer higher current capacity, there's a risk of overloading circuits if too many devices are connected and operated simultaneously.
2. Wiring Complexity: In a parallel circuit, each device or appliance is connected directly to the power source, resulting in a more intricate wiring system throughout the building. This complexity can make troubleshooting and maintenance more challenging.

## Electric Power

Electric power is the rate at which electrical energy is used or consumed in an electrical circuit. It is measured in watts (W) and represents the rate of doing work or the rate of energy transfer within the circuit. Electric power is a crucial concept in understanding and analysing electrical circuits and devices. It is denoted by the symbol P. The formula for electric power is defined as:

Where:
P represents electric power.
W stands for the work done by the electric current.
t represents the time taken for the work to be completed.

Unit of Power: The unit of power is the watt (W), which is derived from the standard units of work (joule) and time (second). Therefore, 1 watt is equivalent to the consumption of 1 joule of energy in 1 second:

In practical applications, particularly for larger systems and appliances, the kilowatt (kW) is frequently used.
1 kilowatt (1 kW) = 1000 watts

### Formula for Calculating Electric Power

We know that

the amount of work (W) performed by an electric current (I) as it flows through a circuit for a duration (t) under the influence of a potential difference (V) can be expressed as follows:

Putting this value of W in equation (1), we get:

Where:
P is the electric power in watts (W).
V is the potential difference (voltage) across the device or circuit in volts (V).
I is the current flowing through the device or circuit in amperes (A).

In other words, the power in watts is equal to the product of the voltage (in volts) and the current (in amperes).

### Alternative Formulas for Electric Power

In addition to the basic formula P = V × I, there are two more formulae for calculating electric power, which are particularly useful when you have information about voltage, current, and resistance. These formulae are derived from Ohm's law:

1. Power (P) in terms of Current (I) and Resistance (R):

Power can be can expressed using the equation:
P = V × I ... (1)

From Ohm’s law we know,
V/I = R
or V = I × R

Putting this value of V in equation (1), we get :
P = I × R × I
P = I2 × R

This formula shows that power is directly proportional to both the square of the current and the resistance. If either the current or the resistance increases, the power also increases significantly.

2. Power (P) in terms of Voltage (V) and Resistance (R):

We know that :
P = V × I ... (1)
From Ohm’s law we have,
V/I = R
or I = V/R

Putting this value of I in equation (1), we get :
P = V x V/R
P = V2/R

In this formula, power is directly proportional to the square of the voltage but inversely proportional to resistance. If the voltage increases, the power increases significantly, but if the resistance increases, the power decreases significantly.

## Electrical Energy

Electrical energy is the energy consumed or used by an electrical device or appliance over a period of time. It is a measure of the total work done or the total amount of energy transferred in an electrical circuit. Electrical energy is commonly measured in units such as watt-hours (Wh) and kilowatt-hours (kWh).

### Formula for Calculating Electrical Energy

The formula for calculating electrical energy (E) is given by the product of the power (P) of the electrical device or appliance and the time (t) for which it is used:

E = P × t

Where:
E is the electrical energy in watt-hours (Wh) or kilowatt-hours (kWh).
P is the power rating of the electrical device in watts (W) or kilowatts (kW).
t is the time in hours (h) for which the device is operated.

This formula allows us to calculate the total electrical energy consumed by an appliance when we know its power rating and the time it operates.

Units of Electrical Energy:

1. Watt-Hour (Wh):One watt-hour (Wh) is the amount of electrical energy consumed when an electrical appliance with a power rating of one watt is used for one hour.
It is a smaller unit of electrical energy, often used for smaller devices and residential electricity billing.
1 Wh = 1 watt × 1 hour
2. Kilowatt-Hour (kWh): The kilowatt-hour (kWh) is a more commonly used unit of electrical energy for commercial and residential electricity billing.
One kilowatt-hour (kWh) is equal to 1000 watt-hours (Wh).
It represents the energy consumed by an electrical appliance with a power rating of one kilowatt when used for one hour.
1 kWh = 1000 Wh

## Heating Effect of Current

The heating effect of current is a phenomenon where electric current flowing through a conductor with resistance generates heat. This effect is widely used in various electrical appliances, such as electric heaters, stoves, toasters, and incandescent light bulbs. The heat produced is the result of the conversion of electrical energy into thermal energy.

Joule's Law of Heating: Joule's law of heating describes the relationship between the heat produced (H), the current (I) passing through a resistor, the resistance (R) of the resistor, and the time (t) for which the current flows. The formula for Joule's law of heating is:

H = I2 x R x t

Where:
H is the heat produced in joules (J).
I is the current in amperes (A).
R is the resistance in ohms (Ω).
t is the time in seconds (s).

The heat produced (H) is directly proportional to the square of the current (I2), resistance (R) and the time (t) for which the current flows.

### Application of the Heating Effect of Current

The heating effect of electric current has several important applications in our daily lives. Here are some notable applications:

1. Electric Heating Appliances: Electric heating appliances like electric irons, electric kettles, electric toasters, electric ovens, room heaters, and water heaters (geysers) utilise the heating effect of current. These appliances contain coils made of high-resistance wires, often composed of nichrome alloy. When current passes through these coils, they become red-hot and produce heat. This heat is used for various purposes, such as ironing clothes, heating water, toasting bread, cooking food, and providing warmth in a room.

Example: An electric iron's heating element, typically made of nichrome wire, becomes red-hot when a current passes through it, allowing it to generate heat for ironing clothes.
2. Incandescent Light Bulbs: Incandescent light bulbs, commonly used for lighting, also rely on the heating effect of current. They consist of a thin tungsten filament with high resistance. When current flows through the filament, it becomes white-hot and emits light. However, a significant portion of the electrical energy is converted into heat rather than visible light, making incandescent bulbs less energy-efficient.
Example: When you turn on an incandescent light bulb, the filament inside becomes white-hot, producing both light and heat.
3. Fuses: Fuses are safety devices used to protect electrical circuits and appliances from excessive current. A fuse typically consists of a short length of thin copper wire with a low melting point. The fuse wire has a higher resistance than the rest of the circuit. If the current in the circuit exceeds a safe limit, the fuse wire heats up and melts, breaking the circuit. This prevents overheating of wires and protects appliances from damage or fire.
Example: In a household electrical circuit, if there's a sudden surge in current due to a fault, the fuse will blow (melt), disconnecting the circuit and preventing potential hazards.
4. Electric Cooktops and Stoves: Electric cooktops and stoves use the heating effect of current to cook food. These appliances have heating elements, often made of nichrome, which become hot when current passes through them. The heat generated by the elements is transferred to pots and pans, cooking the food.
Example: An electric cooktop has heating coils that become red-hot when turned on, allowing you to cook food in pots and pans placed on top.
5. Electric Heaters: Electric heaters, including space heaters and radiant heaters, rely on the heating effect of current to provide warmth. They contain heating elements that become hot when current flows through them, emitting heat into the surrounding space.
Example: A radiant electric heater has a heating element that produces heat when electricity passes through it, warming up a room.