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

Introduction to Electricity

Welcome, students! Electricity is a cornerstone of modern civilization. Imagine a day without it – no lights, no fans, no computers, no smartphones. Life as we know it would come to a standstill. This invisible force powers our world, making it one of the most significant discoveries in human history. In this chapter from the Class 10 NCERT Science syllabus, we will embark on a journey to understand this fundamental form of energy. We will explore what constitutes electricity, how it flows, what governs its movement, and how we harness its power and heating effects in our daily lives. From the simple flow of charge in a wire to the complex wiring in our homes, this chapter lays the foundation for understanding the principles that run our world. Let's demystify the concepts of electric current, potential difference, resistance, and power, one step at a time.

Electric Current and Circuit

The very first concept we need to grasp is the idea of electric charge. You might remember from earlier classes that matter is made of atoms, which contain charged particles: positively charged protons and negatively charged electrons. The flow of these electric charges is what we call an electric current. Typically, in metallic conductors like copper wires, it is the negatively charged electrons that are free to move and constitute the current.

What is Electric Current?

Electric current is formally defined as the rate of flow of net electric charge through any cross-section of a conductor. In simpler terms, it's the amount of charge flowing through a point in a circuit in one second.

If a net charge Q flows through a cross-section of a conductor in time t, then the current I is given by the formula:

I = Q / t

• The SI unit of electric charge (Q) is the coulomb (C). One coulomb is equivalent to the charge contained in approximately 6.25 × 10¹⁸ electrons.
• The SI unit of electric current (I) 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. That is, 1 A = 1 C/s. Smaller units of current are milliampere (1 mA = 10⁻³ A) and microampere (1 µA = 10⁻⁶ A).

An instrument called an ammeter is used to measure the electric current in a circuit. To measure the total current flowing through a circuit, the ammeter must be connected in series, so that all the charge flowing through the circuit also flows through the ammeter.

What is an Electric Circuit?

For the electric current to flow, it needs a continuous and closed path. This path is called an electric circuit. A typical simple electric circuit consists of:

• A source of electricity: Such as a cell or a battery (a combination of cells).
• A load: An electrical component or device that consumes energy, like a bulb or a fan.
• Conducting wires: Usually made of copper or aluminum, to connect the components.
• A switch or key: To open or close the circuit, allowing us to control the flow of current.

When the switch is closed, the circuit is complete, and current flows. When the switch is open, there is a break in the path, and the current stops flowing. By convention, the direction of electric current (known as conventional current) is taken as the direction of flow of positive charge, which is from the positive terminal to the negative terminal of the cell. However, the actual flow of charge in a metallic conductor is the flow of electrons, which move from the negative terminal to the positive terminal. For all practical purposes and circuit diagrams, we use the direction of conventional current.

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. Think of it like water flowing in a pipe. Water only flows if there is a difference in pressure or height between two points. Similarly, electric charges will only flow between two points in a conductor if there is a difference in 'electric pressure' between them. This 'electric pressure' is called the electric potential difference.

Understanding Electric Potential

Electric potential at a point is the work done in moving a unit positive charge from infinity to that point in an electric field. However, in circuits, the more practical and important concept is the difference in potential between two points.

Potential Difference

The potential difference (V) between two points in an electric circuit carrying some current is defined as the work done (W) to move 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 defined as the potential difference between two points in a current-carrying conductor when 1 joule of work is done to move a charge of 1 coulomb from one point to the other. That is, 1 V = 1 J/C.

The potential difference is maintained by a source like a cell or a battery. The chemical reactions inside a cell generate the potential difference across its terminals, which sets the charges in motion in the circuit. An instrument called a voltmeter is used to measure the potential difference. A voltmeter is always connected in parallel across the two points between which the potential difference is to be measured. This is because a voltmeter has very high resistance, and connecting it in parallel ensures it draws negligible current from the main circuit, thus not altering the potential difference it is intended to measure.

Circuit Diagrams

Drawing realistic pictures of batteries, bulbs, and wires for every circuit is cumbersome. Scientists use standardized symbols to represent common electrical components, making it easy to draw and understand circuit diagrams. These diagrams are called schematic diagrams.

Symbols for Common Electrical Components

Here are some of the most frequently used symbols in circuit diagrams:

Ohm's Law

In 1827, German physicist Georg Simon Ohm found a fundamental relationship between the potential difference across a conductor and the current flowing through it. This relationship is known as Ohm's Law and is one of the most important laws in electricity.

Statement and Formula

Ohm's Law states that the potential difference (V) across the ends of a given metallic conductor 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 / I = constant

This constant of proportionality is called Resistance (R).

Thus, the formula for Ohm's Law is:

V = IR

Resistance is the property of a conductor that opposes or resists the flow of electric charges (current) through it. The SI unit of resistance is the ohm, and its symbol is the Greek letter omega (Ω).

From the formula, 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. So, 1 Ω = 1 V / 1 A.

Verification of Ohm's Law

Ohm's law can be verified experimentally by setting up a circuit with a resistor, a battery, an ammeter (in series), a voltmeter (in parallel with the resistor), and a rheostat (variable resistor) to change the current. By varying the resistance of the rheostat, we can obtain different readings for current (I) and potential difference (V). If we plot a graph of V (on the y-axis) against I (on the x-axis), we will get a straight line passing through the origin. This linear relationship confirms Ohm's Law. The slope of this V-I graph gives the value of the resistance (Slope = V/I = R).

Factors on which the Resistance of a Conductor Depends

The resistance of a conductor is not the same for all materials or all shapes. It depends on four key factors:

1. Length of the Conductor (l)

The resistance of a uniform conductor is directly proportional to its length. A longer wire offers more resistance to the flow of electrons than a shorter wire of the same material and thickness.

R ∝ l

2. Area of Cross-section (A)

The resistance of a conductor is inversely proportional to its area of cross-section. A thicker wire (larger area) provides an easier path for electrons to flow, thus offering less resistance.

R ∝ 1/A

3. Nature of the Material (Resistivity)

Different materials have different abilities to conduct electricity. This intrinsic property of a material that determines its resistance is called resistivity or specific resistance, denoted by the Greek letter rho (ρ).

Combining the first two factors, we get: R ∝ l/A.

To turn this proportionality into an equation, we introduce the constant of proportionality, resistivity (ρ):

R = ρ (l/A)

Resistivity (ρ) is defined as the resistance of a conductor of unit length and unit cross-sectional area. Its SI unit is the ohm-meter (Ω m).

• Conductors like metals and alloys have very low resistivity (in the range of 10⁻⁸ Ω m to 10⁻⁶ Ω m). Silver is the best conductor of electricity.
• Insulators like rubber, glass, and plastic have very high resistivity (in the range of 10¹² Ω m to 10¹⁷ Ω m), making them poor conductors.
• Alloys generally have higher resistivity than their constituent metals. This property, along with their high melting points, makes them suitable for use in heating elements of devices like electric irons and toasters (e.g., Nichrome).

4. Temperature

The resistance of most pure metallic conductors increases with an increase in temperature. However, the resistance of alloys like nichrome and manganin is almost unaffected by changes in temperature. This is why they are used to make standard resistance coils.

Resistance of a System of Resistors

In many practical circuits, we 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 two or more resistors are connected end-to-end consecutively, they are said to be connected in series. In a series combination:

• The total current (I) flowing through the circuit remains the same for 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 + ...).

Let's consider three resistors R₁, R₂, and R₃ connected in series to a battery of voltage V. The total or equivalent resistance (Rₛ) of the combination can be derived as follows:

Total voltage V = V₁ + V₂ + V₃

Using Ohm's Law (V = IR) for each resistor: V₁ = IR₁, V₂ = IR₂, V₃ = IR₃.

And for the entire circuit: V = IRₛ.

Substituting these values into the voltage equation:

IRₛ = IR₁ + IR₂ + IR₃

Dividing by I on both sides, we get:

Rₛ = R₁ + R₂ + R₃ + ...

This means that the equivalent resistance in a series combination is simply the sum of the individual resistances. The equivalent resistance is always greater than the largest individual resistance in the combination.

Resistors in Parallel

When two or more resistors are connected between the same two points, they are said to be connected 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 the sum of the currents flowing through the individual resistors (I = I₁ + I₂ + I₃ + ...).

Let's consider three resistors R₁, R₂, and R₃ connected in parallel to a battery of voltage V. The equivalent resistance (Rₚ) can be derived as follows:

Total current I = I₁ + I₂ + I₃

Using Ohm's Law (I = V/R) for each resistor: I₁ = V/R₁, I₂ = V/R₂, I₃ = V/R₃.

And for the entire circuit: I = V/Rₚ.

Substituting these values into the current equation:

V/Rₚ = V/R₁ + V/R₂ + V/R₃

Dividing by V on both sides, we get:

1/Rₚ = 1/R₁ + 1/R₂ + 1/R₃ + ...

This means that the reciprocal of the equivalent resistance in a parallel combination is the sum of the reciprocals of the individual resistances. The equivalent resistance is always smaller than the smallest individual resistance in the combination. Household electrical wiring is a prime example of a parallel circuit, as it allows each appliance to be operated independently at the same voltage.

Heating Effect of Electric Current

When an electric current flows through a resistor, the resistor gets hot. This is because the source of energy (the battery) has to do work to maintain the current against the resistance. This work done by the source gets converted into heat energy, which dissipates in the resistor. This phenomenon is known as the heating effect of electric current, also called Joule heating.

Joule's Law of Heating

The amount of heat produced in a resistor is governed by Joule's Law of Heating. Let's derive the formula. The work done (W) in moving a charge Q through a potential difference V is W = VQ. The power input to the circuit is P = W/t = VQ/t. Since I = Q/t, we have P = VI.

The energy supplied to the circuit by the source in time t is E = P × t = VIt. Assuming all this electrical energy is converted into heat energy (H), we have:

H = VIt

Now, using Ohm's Law (V = IR), we can substitute V in the above equation:

H = (IR)It

H = I²Rt

This is the mathematical expression for Joule's Law of Heating. It states that the heat produced in a resistor is:

• Directly proportional to the square of the current (I²) for a given resistance.
• Directly proportional to the resistance (R) for a given current.
• Directly proportional to the time (t) for which the current flows.

Practical Applications of Heating Effect

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

• Electric Heating Appliances: Devices like electric irons, toasters, ovens, and water heaters work on this principle. They use a heating element made of an alloy like nichrome, which has high resistivity and a high melting point, allowing it to get very hot without melting.
• Electric Bulb: An incandescent bulb produces light due to the heating effect. Its filament is made of tungsten, a metal with a very high melting point (3380 °C). When current passes through it, it gets extremely hot and emits light. The bulb is filled with an inert gas like nitrogen or argon to prevent the filament from burning out.
• Electric Fuse: A fuse is a crucial 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 appliance. If a current larger than a specified value flows through the circuit (due to overloading or short-circuiting), the heat produced (I²Rt) melts the fuse wire, breaking the circuit and protecting the appliance from damage.

Electric Power

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

Defining Electric Power

We know that Power (P) = Work done (W) / time (t).

Since W = VIt, we have P = VIt / t.

P = VI

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

Substitute V = IR in P = VI: P = (IR)I = I²R

Substitute I = V/R in P = VI: P = V(V/R) = V²/R

So, we have three key formulas for electric power: P = VI, P = I²R, and P = V²/R.

Unit of Power and Commercial Unit of Energy

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. Thus, 1 W = 1 volt × 1 ampere.

Since the watt is a small unit, a larger unit called the kilowatt (kW) is often used (1 kW = 1000 W).

Electrical energy is power multiplied by time (E = P × t). Its SI unit is the joule (J). However, the joule is a very small unit for commercial purposes. Therefore, the commercial unit of electrical energy is the kilowatt-hour (kWh), commonly known as a 'unit'.

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

Let's find the relationship between kWh and joules:

1 kWh = 1 kW × 1 h

1 kWh = 1000 W × 3600 s

1 kWh = 3,600,000 Ws

Since 1 watt-second = 1 joule,

1 kWh = 3.6 × 10⁶ J

Important Questions and Answers

Question 1: An electric iron of resistance 20 Ω takes a current of 5 A. Calculate the heat developed in 30 s.

Answer:

Given:

• Resistance (R) = 20 Ω
• Current (I) = 5 A
• Time (t) = 30 s

We need to find the heat developed (H).

According to Joule's Law of Heating, the formula for heat developed is:

H = I²Rt

Substituting the given values into the formula:

H = (5 A)² × 20 Ω × 30 s

H = 25 × 20 × 30

H = 500 × 30

H = 15000 J

The heat developed can also be expressed in kilojoules (kJ): H = 15 kJ.

Therefore, the heat developed in the electric iron is 15,000 joules.

Question 2: An electric bulb is rated 220 V and 100 W. When it is operated on 110 V, what will be the power consumed?

Answer:

This is a two-step problem. First, we need to find the resistance of the bulb using its rating. The resistance of the bulb remains constant.

Step 1: Calculate the resistance of the bulb.

Given rating:

• Voltage (V) = 220 V
• Power (P) = 100 W

We use the power formula that relates P, V, and R: P = V²/R

Rearranging the formula to find R: R = V²/P

R = (220 V)² / 100 W

R = (220 × 220) / 100

R = 48400 / 100

R = 484 Ω

Step 2: Calculate the new power consumed at the new voltage.

New operating conditions:

• New Voltage (V') = 110 V
• Resistance (R) = 484 Ω (This remains unchanged)

We use the same power formula again with the new voltage:

New Power (P') = (V')² / R

P' = (110 V)² / 484 Ω

P' = (110 × 110) / 484

P' = 12100 / 484

P' = 25 W

Therefore, when the bulb is operated on 110 V, the power consumed will be 25 watts.

Question 3: Judge the equivalent resistance when the following are connected in parallel – (a) 1 Ω and 10⁶ Ω, (b) 1 Ω, 10³ Ω, and 10⁶ Ω.

Answer:

For resistors connected in parallel, the formula for equivalent resistance (Rₚ) is: 1/Rₚ = 1/R₁ + 1/R₂ + ...

An important property of parallel combinations is that the equivalent resistance is always smaller than the smallest individual resistance.

(a) R₁ = 1 Ω and R₂ = 10⁶ Ω

Let's calculate the exact value:

1/Rₚ = 1/1 + 1/10⁶

1/Rₚ = (10⁶ + 1) / 10⁶

Rₚ = 10⁶ / (10⁶ + 1) = 1000000 / 1000001 ≈ 0.999999 Ω

As we can see, the equivalent resistance is approximately 1 Ω, which is slightly less than the smallest resistance (1 Ω).

(b) R₁ = 1 Ω, R₂ = 10³ Ω, and R₃ = 10⁶ Ω

Again, the equivalent resistance will be less than the smallest individual resistance, which is 1 Ω.

Let's calculate:

1/Rₚ = 1/1 + 1/10³ + 1/10⁶

1/Rₚ = 1 + 0.001 + 0.000001

1/Rₚ = 1.001001

Rₚ = 1 / 1.001001 ≈ 0.999 Ω

In both cases, when a very small resistance is connected in parallel with very large resistances, the equivalent resistance is dominated by and is just slightly less than the smallest resistance.

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

Answer:

The heating elements of electric toasters and irons are made of an alloy (like nichrome) rather than a pure metal for two primary 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 and time, a higher resistance (R) will produce more heat. This high resistivity allows the coil to get very hot and produce the required amount of heat efficiently.
2. High Melting Point and Resistance to Oxidation: At the high temperatures required for these appliances to function, a pure metal would likely melt or rapidly oxidize (react with oxygen in the air) and break. Alloys like nichrome have a very high melting point and are resistant to oxidation even at red-hot temperatures, which gives them a long operational life.

Chapter Summary

Here are the key takeaways from our deep dive into the chapter on Electricity:

• Electric Current (I): The rate of flow of electric charge (I = Q/t). Its SI unit is the Ampere (A).
• Potential Difference (V): The work done to move a unit charge between two points (V = W/Q). Its SI unit is the Volt (V).
• Ohm's Law: States that V ∝ I, or V = IR, where R is the resistance, provided temperature is constant.
• 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 length (l), area of cross-section (A), and the nature of the material (resistivity, ρ), as given by the formula R = ρ(l/A).
• Resistors in Series: The equivalent resistance is the sum of individual resistances (Rₛ = R₁ + R₂ + ...). Current is the same through all resistors.
• Resistors in Parallel: The reciprocal of the equivalent resistance is the sum of the reciprocals of individual resistances (1/Rₚ = 1/R₁ + 1/R₂ + ...). Voltage is the same across all resistors.
• Joule's Law of Heating: The heat produced in a resistor is given by H = I²Rt.
• Electric Power (P): The rate at which electrical energy is consumed. P = VI = I²R = V²/R. Its SI unit is the Watt (W).
• Commercial Unit of Energy: The kilowatt-hour (kWh), where 1 kWh = 3.6 × 10⁶ J.