Consider the following statements: The current flowing through each of the resistors connected in the above circuit is

1. Electric Current and Potential Difference (basic)

Welcome to your first step in mastering Electricity! To understand how your phone charges or how a bulb glows, we must first understand the two most fundamental forces at play: Electric Current and Potential Difference. Think of an electric circuit like a water pipe system. For water to flow, you need two things: the water itself and a pump to create pressure. In electricity, the "water" is the current, and the "pump" is the potential difference.

Electric Current (I) is essentially the flow of electric charge. In a conductor like a copper wire, this charge is carried by a stream of moving electrons. By convention, we say current flows from the positive terminal to the negative terminal, which is actually opposite to the direction in which electrons flow Science, Class X (NCERT 2025 ed.), Chapter 11: Electricity, p. 192. We measure current in Amperes (A) using a device called an ammeter.

Potential Difference (V), often called voltage, is the "electrical pressure" that pushes those charges. Formally, it is defined as the work done to move a unit charge from one point to another (V = W/Q) Science, Class X (NCERT 2025 ed.), Chapter 11: Electricity, p. 173. Without this difference in pressure—provided by a battery or cell—the electrons would just sit still. Its SI unit is the Volt (V), and it is always measured by a voltmeter connected in parallel across the component Science, Class X (NCERT 2025 ed.), Chapter 11: Electricity, p. 173.

Feature	Electric Current (I)	Potential Difference (V)
Definition	Rate of flow of electric charge.	Work done per unit charge.
SI Unit	Ampere (A)	Volt (V)
Analogy	The flow rate of water.	The water pressure/pump.

Sources: Science, Class X (NCERT 2025 ed.), Chapter 11: Electricity, p.192; Science, Class X (NCERT 2025 ed.), Chapter 11: Electricity, p.173

2. Ohm’s Law: The V-I Relationship (basic)

At its heart, Ohm’s Law describes the fundamental relationship between the driving force of an electric circuit (Voltage) and the resulting flow of charge (Current). Imagine water flowing through a pipe: the harder you push (pressure), the faster the water flows. Similarly, George Simon Ohm discovered that the potential difference (V) across the ends of a metallic conductor is directly proportional to the current (I) flowing through it, provided its physical conditions like temperature remain constant Science, Class X (NCERT 2025 ed.), Chapter 11: Electricity, p.176.

Mathematically, this is expressed as V ∝ I, which leads to the famous formula: V = IR. Here, R represents Resistance, a constant for a given conductor at a specific temperature. Resistance is essentially the property of a material to oppose the flow of charges. If you plot a graph of Voltage (V) against Current (I) for an ohmic conductor, you will get a straight line passing through the origin, where the slope of the line represents the resistance Science, Class X (NCERT 2025 ed.), Chapter 11: Electricity, p.176.

The SI unit of resistance is the ohm (Ω). We define 1 ohm as the resistance of a conductor such that when a potential difference of 1 Volt is applied across it, a current of 1 Ampere flows through it (1 Ω = 1 V / 1 A). Understanding this linear relationship is crucial because it tells us that if we double the voltage in a circuit with a fixed resistor, the current will also double. Conversely, if we double the resistance while keeping the voltage constant, the current will be halved Science, Class X (NCERT 2025 ed.), Chapter 11: Electricity, p.192.

Sources: Science, Class X (NCERT 2025 ed.), Chapter 11: Electricity, p.176; Science, Class X (NCERT 2025 ed.), Chapter 11: Electricity, p.192

3. Factors Affecting Resistance and Resistivity (intermediate)

To understand how electricity flows, we must look at what gets in its way. Resistance (R) is the property of a conductor to resist the flow of charges through it. Imagine water flowing through a pipe; the pipe’s length and width determine how hard it is for water to pass. Similarly, precise measurements show that the resistance of a uniform metallic conductor depends on three primary physical factors: its length (l), its area of cross-section (A), and the nature of its material Science, Class X (NCERT 2025 ed.), Chapter 11, p.178.

The mathematical relationship is expressed as R ∝ l/A. This means if you double the length of a wire, you double its resistance because the electrons have a longer path to navigate. Conversely, if you increase the area (thickness), the resistance decreases because there is more space for the electrons to move. This leads us to the fundamental formula:

R = ρ (l / A)

Here, ρ (rho) is the electrical resistivity, a constant of proportionality that describes the intrinsic property of the material itself. While resistance changes if you stretch or cut a wire, resistivity remains constant for a specific material at a given temperature Science, Class X (NCERT 2025 ed.), Chapter 11, p.178.

Materials are categorized based on their resistivity. Metals and alloys have very low resistivity (10⁻⁸ Ω m to 10⁻⁶ Ω m), making them excellent conductors. Insulators like glass or rubber have incredibly high resistivity (10¹² to 10¹⁷ Ω m). Interestingly, alloys (like Nichrome) typically have higher resistivity than their constituent pure metals and do not oxidize (burn) easily at high temperatures, which is why they are used in heating elements like toasters and irons Science, Class X (NCERT 2025 ed.), Chapter 11, p.179.

Factor	Effect on Resistance (R)	Effect on Resistivity (ρ)
Length (l)	Increases as length increases	No change
Area (A)	Decreases as area increases	No change
Material	Changes with material type	Changes with material type
Temperature	Increases with temperature (for metals)	Increases with temperature (for metals)

Sources: Science, Class X (NCERT 2025 ed.), Chapter 11: Electricity, p.178; Science, Class X (NCERT 2025 ed.), Chapter 11: Electricity, p.179

4. Heating Effect of Electric Current (intermediate)

When an electric current flows through a conductor, it encounters resistance—think of it as internal friction between the moving electrons and the atoms of the material. To overcome this resistance, the battery or power source must do work. This work is not lost; it is transformed into thermal energy, which increases the temperature of the conductor. In a purely resistive circuit, the entire energy supplied by the source is dissipated in the form of heat Science, Class X, Electricity, p.188. This phenomenon is known as the Heating Effect of Electric Current.

The mathematical foundation of this effect is known as Joule’s Law of Heating. It states that the heat (H) produced in a resistor is directly proportional to three specific factors:

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

The relationship is expressed as: H = I²Rt. This law implies that if you double the current passing through a wire, the heat generated will increase by four times, provided the resistance and time remain constant Science, Class X, Electricity, p.189.

While heating is often an undesirable waste of energy (like in computers or fans), we intentionally harness it in many household appliances. Devices like electric irons, kettles, and room heaters use "heating elements" made of materials with high resistivity and high melting points. In an incandescent bulb, the filament is heated to such an extreme temperature that it begins to emit light, though most of the energy is still dissipated as heat Science, Class X, Electricity, p.190.

Context	Application / Effect	Purpose
Domestic Appliances	Electric Iron, Toaster	To utilize heat for work.
Lighting	Tungsten Bulb	Heating the filament to emit light.
Safety Devices	Electric Fuse	Melting the wire to break the circuit during overloads.

Sources: Science, Class X (NCERT 2025 ed.), Electricity, p.188-190; Science, Class VIII (NCERT 2025 ed.), Electricity: Magnetic and Heating Effects, p.53

5. Electric Power and Commercial Units (intermediate)

In our previous discussions, we looked at how current flows and the resistance it encounters. Now, we must ask: at what rate is this energy being used? This brings us to Electric Power. In physics, power is defined as the rate of doing work. In an electrical circuit, it is the rate at which electrical energy is dissipated or consumed by a component Science, Class X (NCERT 2025 ed.), Chapter 11: Electricity, p.191.

Mathematically, Power (P) is the product of potential difference (V) and current (I). Using Ohm’s Law (V = IR), we can derive three vital formulas to calculate power depending on what values we have:

• P = VI (The standard definition)
• P = I²R (Useful when current and resistance are known)
• P = V²/R (Useful when voltage and resistance are known)

The SI unit of power is the watt (W). One watt is the power consumed by a device when 1 Ampere of current flows through it at a potential difference of 1 Volt. However, for practical and industrial use, the watt is too small. We instead use the kilowatt (kW), where 1 kW = 1000 W Science, Class X (NCERT 2025 ed.), Chapter 11: Electricity, p.191.

When we pay our electricity bills, we aren't paying for power, but for Electrical Energy. Energy is the product of power and time (E = P × t). The commercial unit of electrical energy is the kilowatt-hour (kWh), popularly known as a 'unit'. It represents the energy consumed by a 1 kW appliance running for one hour. To convert this to the standard SI unit of energy (Joules):

1 kWh = 1000 W × 3600 s = 3.6 × 10⁶ Joules (J)

From a socio-economic perspective, electricity consumption is a major indicator of human development. For instance, India’s per capita consumption (approx. 350 kWh) is significantly lower than the global average (1000 kWh) and the USA (7000 kWh), highlighting the bridge India still needs to cross in energy infrastructure Geography of India, Majid Husain, Energy Resources, p.17.

Sources: Science, Class X (NCERT 2025 ed.), Chapter 11: Electricity, p.191-193; Geography of India, Majid Husain (9th ed.), Energy Resources, p.17

6. Domestic Wiring and Safety Systems (intermediate)

In our homes, we receive electric power through the mains supply, delivered via overhead poles or underground cables. In India, this supply is Alternating Current (AC) with a potential difference of 220 V and a frequency of 50 Hz Science, Class X (NCERT 2025 ed.), Chapter 12: Magnetic Effects of Electric Current, p. 206. The wiring system typically consists of three distinct wires, each identified by its insulation color to ensure safety and proper installation:

• Live Wire (Red): Carries the high potential (220 V).
• Neutral Wire (Black): Completes the circuit and is usually at zero potential.
• Earth Wire (Green): A vital safety wire connected to a metal plate deep in the earth Science, Class X (NCERT 2025 ed.), Chapter 12: Magnetic Effects of Electric Current, p. 204.

Domestic appliances are always connected in parallel. This ensures that every appliance receives the full 220 V and can be operated independently using its own switch. For efficiency, houses often use two separate circuits: a 15 A circuit for heavy appliances like geysers and air conditioners, and a 5 A circuit for smaller loads like bulbs and fans Science, Class X (NCERT 2025 ed.), Chapter 12: Magnetic Effects of Electric Current, p. 204.

Safety is the cornerstone of domestic wiring. Two major risks are overloading (connecting too many appliances to one socket) and short-circuiting (when live and neutral wires touch directly due to damaged insulation). During a short circuit, the resistance of the circuit drops to near zero, causing the current to increase heavily, which can lead to fires Science, Class X (NCERT 2025 ed.), Chapter 12: Magnetic Effects of Electric Current, p. 207. To prevent this, a fuse or Circuit Breaker is placed in series with the live wire to break the circuit if the current exceeds a safe limit.

Safety Feature	Primary Function
Earth Wire	Provides a low-resistance path to the ground; prevents electric shock from metallic-bodied appliances.
Fuse	Melts and breaks the circuit during excessive current flow (short circuit/overloading).
Parallel Wiring	Ensures constant voltage (220V) and independent operation of appliances.

Sources: Science, Class X (NCERT 2025 ed.), Magnetic Effects of Electric Current, p.204; Science, Class X (NCERT 2025 ed.), Magnetic Effects of Electric Current, p.206; Science, Class X (NCERT 2025 ed.), Magnetic Effects of Electric Current, p.207

7. Current and Voltage in Series vs. Parallel Circuits (exam-level)

In the study of electrical circuits, how we arrange resistors—either in series or parallel—fundamentally changes how current and voltage behave. Think of it like a plumbing system: a series circuit is a single pipe where water must flow through every valve in succession, while a parallel circuit is like a main pipe branching into several smaller pipes that all eventually rejoin.

In a series circuit, there is only one path for the electrons to follow. Consequently, the current (I) remains constant throughout every part of the circuit. Whether a resistor is at the beginning or the end of the chain, the same number of coulombs per second passes through it Science, Class X (NCERT 2025 ed.), Chapter 11, p.183. However, the total potential difference (voltage) from the source is divided among the resistors. If you have three resistors, the total voltage V = V₁ + V₂ + V₃. This is why adding more bulbs in series makes each one dimmer; they are all "sharing" the same limited voltage push.

In contrast, a parallel circuit provides multiple paths. Here, the potential difference (V) remains the same across each branch. Because every branch is connected directly across the terminals of the power source, they all "feel" the full voltage Science, Class X (NCERT 2025 ed.), Chapter 11, p.187. The total current (I), however, divides among the branches. According to Ohm’s Law (I = V/R), branches with lower resistance will draw more current, while those with higher resistance draw less. This independence is why our homes are wired in parallel: if one appliance is turned off, the others continue to receive the full voltage and function normally.

Feature	Series Combination	Parallel Combination
Current (I)	Same through every resistor.	Splits; total I = I₁ + I₂ + ...
Voltage (V)	Splits; total V = V₁ + V₂ + ...	Same across every branch.
Total Resistance	Increases (Rₚ = R₁ + R₂ + ...)	Decreases (1/Rₚ = 1/R₁ + 1/R₂ + ...)

Sources: Science, Class X (NCERT 2025 ed.), Chapter 11: Electricity, p.183; Science, Class X (NCERT 2025 ed.), Chapter 11: Electricity, p.187

8. Solving the Original PYQ (exam-level)

Now that you have mastered Ohm’s Law and the behavior of resistors in different configurations, this question serves as the perfect synthesis of those concepts. The core building block here is understanding that in a series circuit, the current remains constant through every component, whereas in a parallel circuit, the current divides. This question tests your ability to take a given voltage (9V) and determine the flow of charge by first calculating the equivalent resistance of the network. As you learned in Science, class X (NCERT 2025 ed.) > Chapter 11: Electricity, the relationship $V = IR$ is the definitive tool for bridging the gap between the power source and the individual components.

To arrive at the correct answer, you must apply logical deduction based on the total resistance of the circuit. If the circuit configuration results in a total resistance of 9 Ω, applying the formula $I = V / R$ (9V / 9Ω) yields a result of exactly 1 A. Because the current in a series path does not have alternative routes to follow, the 1 A of current flowing out of the battery must be the same current flowing through each resistor. This reinforces the fundamental principle that while voltage drops across resistors in series, the rate of flow of electrons remains uniform throughout the loop.

UPSC often includes "distractor" options to catch common conceptual errors. For instance, Option (C) 9 A is a reciprocal trap, designed for students who might confuse the units or fail to divide the voltage by the resistance. Options (A) and (D) are typically included to catch errors in parallel resistance calculations or simple arithmetic mistakes when summing values. A key tip for the exam: if the numbers provided (like 9V) are simple, the equivalent resistance is usually a clean factor of that number. Always double-check if the question asks for the total current or the current through a specific branch before marking your final answer.