NCERT Class 10 Science Chapter 12: Electricity - A Complete Guide

Introduction to Electricity

Welcome, students, to a comprehensive exploration of one of the most fundamental and transformative forms of energy in our modern world: Electricity. Chapter 12 of your NCERT Class 10 Science textbook delves into this fascinating topic. Think about your daily life for a moment. The lights in your room, the fan that cools you, the television you watch, the computer you use for your studies, and the mobile phone that connects you to the world – all of these are powered by electricity. It has become an indispensable part of our civilization, driving industries, homes, and technological advancements. But what exactly is this invisible force? How does it travel through wires to power our devices? What principles govern its behavior? This chapter provides the answers to these very questions. We will start by understanding the basics of electric charge and current, move on to the concepts of potential difference and resistance, explore the crucial Ohm's Law, and finally, study the heating effects of current and the concept of electric power. Mastering these concepts is not just crucial for your board exams but also for building a strong foundation in physics and understanding the technology that shapes our lives. Let's embark on this electrifying journey together!

Electric Current and Circuit

The very first step to understanding electricity is to grasp the concept of electric charge and how its movement constitutes an electric current within a defined path called a circuit.

What is Electric Charge?

At the heart of all electrical phenomena is the fundamental property of matter known as electric charge. You have already learned that matter is made of atoms, which in turn consist of protons, neutrons, and electrons. Protons are positively charged, electrons are negatively charged, and neutrons are neutral. In most stable materials, the number of protons and electrons is equal, making the object electrically neutral. However, electrons, particularly the outermost ones, can sometimes be removed from or added to an atom. An object becomes positively charged if it loses electrons and negatively charged if it gains electrons. The SI unit of electric charge is the coulomb (C). One coulomb is equivalent to the charge contained in approximately 6.25 × 10¹⁸ electrons. The charge on a single electron is a fundamental constant, which is -1.602 × 10^-19 C.

Electric Current

Imagine a river. The flow of water in the river is what we call a water current. Similarly, the flow of electric charge through a conductor is called an electric current. It is the rate at which charge flows. If a net charge 'Q' flows across any cross-section of a conductor in time 't', then the current 'I' is given by:

I = Q / t

The SI unit of electric current is the ampere (A), named after the French scientist André-Marie Ampère. One ampere is defined as the flow of one coulomb of charge per second (1 A = 1 C/s). Small currents are often expressed in milliamperes (1 mA = 10^-3 A) or microamperes (1 µA = 10^-6 A). An instrument called an ammeter is used to measure the electric current in a circuit. It is always connected in series in the circuit so that the entire current to be measured flows through it.

Electric Circuit

For an electric current to flow, it needs a continuous and closed path. This path is known as an electric circuit. A simple electric circuit consists of a source of electricity (like a cell or battery), a load or device that consumes electricity (like a bulb), connecting wires (usually made of copper), and a switch or key to open or close the circuit. When the switch is closed, the path is complete, and current flows, causing the bulb to light up. This is a closed circuit. When the switch is open, there is a break in the path, the current stops flowing, and the bulb goes off. This is an open circuit.

An interesting point to note is the direction of current. Historically, when the phenomenon of electricity was first discovered, electrons were not known. Scientists assumed that the current was due to the flow of positive charges. Thus, the direction of conventional current was taken as the direction of flow of positive charge, which is from the positive terminal to the negative terminal of a battery. In reality, in metallic conductors, it is the negatively charged electrons that flow from the negative terminal to the positive terminal. However, for the sake of convention, we still consider the direction of current to be opposite to the direction of the flow of electrons.

Electric Potential and Potential Difference

Why do charges flow in a conductor? What makes them move? The answer lies in the concept of electric potential difference, which is analogous to a pressure difference that causes water to flow in a pipe.

Understanding Electric Potential

Consider two water tanks connected by a pipe at the bottom. If both tanks have water at the same level, no water will flow through the pipe. However, if one tank has a higher water level than the other, water will flow from the higher level to the lower level until the levels become equal. This difference in water level creates a pressure difference.

Similarly, for charges to flow between two points in a conductor, there must be a difference in 'electric pressure' between those points. This electric pressure difference is known as the potential difference. This difference in potential is created by a source of energy, like a cell or a battery. The chemical reactions inside a cell generate a potential difference across its terminals, which sets the charges in motion in the circuit.

Potential Difference

The potential difference (V) between two points in an electric circuit is defined as the work done (W) in moving a unit charge (Q) from one point to the other.

V = W / Q

The SI unit of potential difference is the volt (V), named after the Italian physicist Alessandro Volta. One volt is the potential difference between two points when 1 joule of work is done to move a charge of 1 coulomb from one point to the other (1 V = 1 J/C). Potential difference is measured using an instrument called a voltmeter. A voltmeter is always connected in parallel across the two points between which the potential difference is to be measured.

Circuit Diagrams

Drawing realistic pictures of circuits is cumbersome. Therefore, we use schematic diagrams where different components of the circuit are represented by standard symbols. This makes it easy to draw and understand circuits.

Commonly Used Circuit Symbols

Ohm's Law

One of the most fundamental laws in electricity is Ohm's law, which establishes a relationship between the potential difference across a conductor and the current flowing through it.

German physicist Georg Simon Ohm found that for many types of materials, the current is directly proportional to the voltage. Ohm's law states that the potential difference (V) across the ends of a given metallic wire in an electric circuit is directly proportional to the current (I) flowing through it, provided its temperature remains the same.

Mathematically, this can be expressed as:

V ∝ I

or

V = IR

Here, R is a constant for the given conductor at a given temperature and is called its resistance.

Resistance (R)

Resistance is the property of a conductor to resist or oppose the flow of charges through it. When electrons move through a conductor, they collide with the atoms and ions present in it. These collisions obstruct the flow of electrons and give rise to resistance. The SI unit of resistance is the ohm (Ω). From Ohm's law, R = V/I. Therefore, 1 ohm is the resistance of a conductor if a potential difference of 1 volt across its ends causes a current of 1 ampere to flow through it (1 Ω = 1 V/A). A component used to provide a specific amount of resistance in a circuit is called a resistor. A component with variable resistance is called a rheostat, which is used to regulate the current without changing the voltage source.

Factors on which the Resistance of a Conductor Depends

The resistance of a conductor is not the same for all materials or all situations. It depends on several factors:

• Length of the conductor (l): The resistance (R) is directly proportional to the length of the conductor. A longer wire offers more resistance than a shorter wire, just as a long, narrow pipe offers more resistance to water flow than a short one. (R ∝ l)
• Area of cross-section (A): The resistance (R) is inversely proportional to the area of cross-section. A thicker wire has a larger cross-sectional area and thus offers less resistance than a thin wire. (R ∝ 1/A)
• Nature of the material: Different materials have different resistances. For example, copper has very low resistance, making it an excellent conductor, while nichrome has a higher resistance. Insulators like rubber have \textremely high resistance.
• Temperature: For most metallic conductors, resistance increases with an increase in temperature.

Resistivity (ρ)

By combining the dependencies on length and area, we get R ∝ l/A. To turn this into an equation, we introduce a constant of proportionality, ρ (rho), called resistivity or specific resistance.

R = ρ (l/A)

Resistivity is a fundamental property of the material itself. It is defined as the resistance of a conductor of unit length and unit cross-sectional area. The SI unit of resistivity is the ohm-meter (Ω m). Conductors like metals and alloys have very low resistivity (10^-8 Ω m to 10^-6 Ω m). Insulators like glass and rubber have very high resistivity (10¹² Ω m to 10¹⁷ Ω m). Alloys generally have higher resistivity than their constituent pure metals, which is why they are used in heating devices like electric irons and toasters.

Resistance of a System of Resistors

In practical circuits, we often need to combine two or more resistors to get a desired value of resistance. Resistors can be combined in two primary ways: in series and in parallel.

Resistors in Series

When resistors are connected end-to-end, they are said to be in series. In a series combination:

• The total current (I) flowing through the circuit remains the same through each resistor.
• The total potential difference (V) across the combination is the sum of the potential differences across the individual resistors (V = V1 + V2 + V3 + ...).

The equivalent resistance of the series combination (Rs) is the sum of the individual resistances:

Rs = R1 + R2 + R3 + ...

The equivalent resistance in a series circuit is always greater than the largest individual resistance. A major disadvantage of series circuits is that if one component fails (e.g., a bulb fuses), the entire circuit is broken, and no current can flow. This is why decorative festival lights often go out completely if a single bulb fails.

Resistors in Parallel

When resistors are connected between two common points, they are said to be in parallel. In a parallel combination:

• The potential difference (V) across each resistor is the same and is equal to the voltage of the source.
• The total current (I) from the source is divided among the parallel branches (I = I1 + I2 + I3 + ...).

The reciprocal of the equivalent resistance of the parallel combination (Rp) is the sum of the reciprocals of the individual resistances:

1/Rp = 1/R1 + 1/R2 + 1/R3 + ...

The equivalent resistance in a parallel circuit is always less than the smallest individual resistance. Domestic wiring is done using parallel circuits. This has two main advantages: (1) Each appliance gets the full mains voltage. (2) If one appliance is switched off or stops working, the others are not affected.

Heating Effect of Electric Current

When an electric current passes through a conductor, the conductor becomes hot. This is known as the heating effect of electric current. This happens because the battery or source has to do work to move the charges against the resistance of the conductor. This work done is converted into heat energy, which raises the temperature of the conductor. This effect is also known as Joule heating.

Joule's Law of Heating

The amount of heat (H) produced in a resistor is given by Joule's law of heating. The law states that the heat produced in a resistor is:

• (i) directly proportional to the square of the current for a given resistance (H ∝ I²),
• (ii) directly proportional to the resistance for a given current (H ∝ R), and
• (iii) directly proportional to the time for which the current flows (H ∝ t).

Combining these, we get the mathematical expression for Joule's law:

H = I²Rt

Since heat is a form of energy, its SI unit is the joule (J).

Practical Applications of Heating Effect

The heating effect of current is utilized in many household appliances:

• Electric Heaters and Irons: These devices have a heating element made of an alloy like nichrome, which has high resistivity and a high melting point. When a large current passes through it, it produces a significant amount of heat.
• Electric Bulb: The filament of an incandescent bulb is made of tungsten, a metal with a very high melting point. When current passes through it, it gets heated to a very high temperature and starts to glow, producing light. Most of the energy is wasted as heat.
• Electric Fuse: A fuse is a safety device used in electric circuits. It consists of a piece of wire made of a metal or an alloy with a low melting point (e.g., an alloy of tin and lead). It is connected in series with the circuit. If the current in the circuit exceeds a safe limit (due to overloading or a short circuit), the heat produced (I²Rt) melts the fuse wire, breaking the circuit and preventing damage to the appliances.

Electric Power

In physics, power is the rate of doing work or the rate of energy consumption. Similarly, electric power (P) is the rate at which electrical energy is consumed or dissipated in an electric circuit.

P = W / t

We know that W = VQ, so P = VQ/t. Since I = Q/t, we get:

P = VI

Using Ohm's law (V = IR), we can also express power in other forms:

P = (IR)I = I²R

P = V(V/R) = V²/R

The SI unit of electric power is the watt (W). One watt is the power consumed by a device that carries 1 A of current when operated at a potential difference of 1 V (1 W = 1 Volt × 1 Ampere). A larger unit of power is the kilowatt (1 kW = 1000 W).

Electrical energy is the product of power and time (E = P × t). The commercial unit of electrical energy is the kilowatt-hour (kWh), often simply called a 'unit'.

1 kWh is the energy consumed when 1 kilowatt of power is used for 1 hour.

1 kWh = 1000 W × 3600 s = 3.6 × 10⁶ Ws = 3.6 × 10⁶ J

Our electricity bills are calculated based on the number of kWh or 'units' of energy consumed.

Important Questions and Answers

Here are a few solved questions to help you test your understanding of the chapter.

Question 1: An electric iron draws a current of 3.4 A from the 220 V supply line. What current will this electric iron draw when connected to a 110 V supply line?

Answer: First, we need to find the resistance of the electric iron, which remains constant. Given: V1 = 220 V, I1 = 3.4 A Using Ohm's Law (V = IR), the resistance R = V1 / I1 R = 220 V / 3.4 A ≈ 64.7 Ω Now, the iron is connected to a new supply line. Given: V2 = 110 V The resistance R remains the same (64.7 Ω). Using Ohm's law again to find the new current I2: I2 = V2 / R I2 = 110 V / 64.7 Ω ≈ 1.7 A So, the electric iron will draw a current of 1.7 A from the 110 V supply line.

Question 2: Three resistors of 2 Ω, 3 Ω, and 6 Ω are connected (a) in series and (b) in parallel. Calculate the equivalent resistance in each case.

Answer: Given R1 = 2 Ω, R2 = 3 Ω, R3 = 6 Ω (a) In Series Combination: The equivalent resistance (Rs) is the sum of individual resistances. Rs = R1 + R2 + R3 Rs = 2 Ω + 3 Ω + 6 Ω = 11 Ω (b) In Parallel Combination: The reciprocal of the equivalent resistance (Rp) is the sum of the reciprocals of individual resistances. 1/Rp = 1/R1 + 1/R2 + 1/R3 1/Rp = 1/2 + 1/3 + 1/6 To add these fractions, we find the common denominator, which is 6. 1/Rp = (3/6) + (2/6) + (1/6) 1/Rp = (3+2+1)/6 = 6/6 = 1 Rp = 1 Ω

Question 3: An electric heater of resistance 8 Ω draws 15 A from the service mains for 2 hours. Calculate the rate at which heat is developed in the heater.

Answer: The rate at which heat is developed is simply the electric power (P). Given: R = 8 Ω, I = 15 A We use the formula for power: P = I²R P = (15 A)² × 8 Ω P = 225 A² × 8 Ω = 1800 W P = 1.8 kW Thus, heat is developed in the heater at a rate of 1800 joules per second, or 1800 W.

Question 4: Why are the coils of electric toasters and electric irons made of an alloy rather than a pure metal?

Answer: The heating elements of appliances like toasters and irons are made of an alloy (like nichrome) for two main reasons:

1. High Resistivity: Alloys have a much higher resistivity than their constituent pure metals. According to Joule's law of heating (H = I²Rt), for a given current, a higher resistance produces more heat.
2. High Melting Point and Resistance to Oxidation: Alloys have a high melting point and do not oxidize (or burn) easily even at very high temperatures. This ensures that the heating element can be heated to a high temperature to provide sufficient heat without melting or getting damaged.

Chapter Summary

Let's quickly recap the key concepts from this chapter:

• Electric Current (I): The rate of flow of electric charge (Q). I = Q/t. Its SI unit is the Ampere (A).
• Potential Difference (V): Work done per unit charge. V = W/Q. Its SI unit is the Volt (V).
• Ohm's Law: At constant temperature, the current through a conductor is directly proportional to the potential difference across its ends. V = IR.
• Resistance (R): The property of a conductor to oppose the flow of current. Its SI unit is the Ohm (Ω).
• Factors Affecting Resistance: Resistance depends on the material's length (l), area of cross-section (A), and its resistivity (ρ). R = ρ(l/A).
• Resistors in Series: Current is the same, voltage adds up. Equivalent resistance Rs = R1 + R2 + R3.
• Resistors in Parallel: Voltage is the same, current divides. Equivalent resistance 1/Rp = 1/R1 + 1/R2 + 1/R3.
• Joule's Law of Heating: Heat produced in a resistor is H = I²Rt.
• Electric Power (P): The rate of consumption of electrical energy. P = VI = I²R = V²/R. Its SI unit is the Watt (W).
• Commercial Unit of Energy: The kilowatt-hour (kWh). 1 kWh = 3.6 × 10⁶ J.