If the current in an electric bulb drops by 1 per cent, the power decreases, approximately by

1. Basics of Electric Current and Potential Difference (basic)

To understand the foundation of electricity, we must first look at what happens inside a conductor, like a copper wire. Electric current is essentially the flow of electric charges. In metallic wires, these charges are electrons. While we often think of electricity as a static thing, it is actually a dynamic process where a stream of electrons moves through a conductor to constitute a current Science, Class X, Chapter 11, p. 192. Interestingly, by historical convention, the direction of electric current is considered to be opposite to the direction of the flow of electrons—moving from the positive terminal to the negative terminal of a circuit.

But why do these electrons move at all? They require a "push" or a difference in "pressure." This is where Potential Difference (V) comes in. Imagine water in a horizontal tube; it won't flow unless there is a pressure difference between the ends. Similarly, to set electrons in motion, we use a cell or a battery to create a potential difference across the terminals Science, Class X, Chapter 11, p. 192. This difference is measured in Volts (V), while the current itself is measured in Amperes (A) Science, Class X, Chapter 11, p. 176.

The relationship between these two can be summarized as follows:

Sources: Science, Class X, Chapter 11: Electricity, p.171; Science, Class X, Chapter 11: Electricity, p.176; Science, Class X, Chapter 11: Electricity, p.192

2. Ohm’s Law and Electrical Resistance (basic)

3. Heating Effect of Electric Current (Joule's Law) (intermediate)

When we talk about the Heating Effect of Electric Current, we are looking at the conversion of electrical energy into thermal energy. At a microscopic level, as electrons drift through a conductor, they constantly collide with the atoms and ions of the material. These collisions transfer kinetic energy to the atoms, causing them to vibrate more vigorously, which we observe as an increase in temperature Science, Class X, Chapter 11, p.190. While this is often seen as a waste of energy in gadgets like computers (which require cooling fans), it is the very principle that makes our electric kettles, irons, and toasters work.

To quantify this effect, we look to Joule’s Law of Heating. This law establishes that the heat (H) produced in a resistor is governed by three specific factors:

• Square of the Current (I²): Heat is directly proportional to the square of the current for a given resistance. This means if you double the current, the heat produced doesn't just double—it increases by four times (2² = 4).
• Resistance (R): Heat is directly proportional to the resistance for a given current. A higher resistance material will generate more heat than a low-resistance one Science, Class X, Chapter 11, p.189.
• Time (t): Heat is directly proportional to the duration for which the current flows.

Mathematically, this is expressed as H = I²Rt. In terms of Power (P), which is the rate at which heat is produced, we use the formula P = I²R. This relationship is crucial for engineers; for instance, in high-temperature industrial furnaces used to melt steel, precise control of current is necessary to reach the extreme temperatures required Curiosity — Textbook of Science for Grade 8, Chapter 4, p.54. Because the power depends on the square of the current, even small fluctuations in the current can lead to significant changes in the heat output of an appliance.

Sources: Science, Class X (NCERT 2025 ed.), Chapter 11: Electricity, p.189, 190; Curiosity — Textbook of Science for Grade 8, Chapter 4: Electricity, p.54

4. Domestic Electric Circuits and Safety Devices (intermediate)

In our homes, the electricity we use is distributed through a sophisticated network designed for both convenience and safety. A standard domestic circuit typically consists of three types of wires: the Live wire (usually red insulation), the Neutral wire (black insulation), and the Earth wire (green insulation). To ensure that every appliance receives the same standard voltage (220 V in India) and can be operated independently, appliances are always connected in parallel Science, Class X (NCERT 2025 ed.), Chapter 12, p.205. This parallel arrangement is crucial because if one appliance fails or is switched off, the rest of the circuit remains functional, unlike a series circuit where a single break would stop the current for everything.

Safety is managed primarily through two mechanisms: the Electric Fuse and Earthing. A fuse is a safety device connected in series with the circuit. It contains a wire with a specific melting point; if the current exceeds a safe limit (due to short-circuiting or overloading), the wire melts due to Joule heating, breaking the circuit and protecting your expensive appliances Science, Class X (NCERT 2025 ed.), Chapter 11, p.190. Meanwhile, the Earth wire serves as a low-resistance path to the ground. It is connected to the metallic bodies of appliances like refrigerators or irons to ensure that any leakage of current doesn't give the user a severe shock Science, Class X (NCERT 2025 ed.), Chapter 12, p.206.

From a mathematical perspective, it is interesting to note how sensitive our appliances are to current fluctuations. Since power (P) is proportional to the square of the current (I²R), even a minor change in current has a doubled impact on power. For instance, if the current flowing through a heating element drops by just 1%, the power output—and thus the heat generated—decreases by approximately 2% Science, Class X (NCERT 2025 ed.), Chapter 11, p.189. This relationship explains why safety devices must be highly precise in monitoring current flow.

Sources: Science, Class X (NCERT 2025 ed.), Chapter 12: Magnetic Effects of Electric Current, p.205-206; Science, Class X (NCERT 2025 ed.), Chapter 11: Electricity, p.189-190

5. Commercial Unit of Energy and Power Rating (intermediate)

In our journey through electricity, we often talk about Power (the rate of doing work) and Energy (the total work done). While the SI unit of energy is the Joule (J), it is too small for practical use in our homes and industries. Imagine measuring your monthly electricity usage in millions of Joules—the numbers would be astronomical! To solve this, we use the Commercial Unit of Energy: the kilowatt-hour (kWh), often simply called a 'unit' on your electricity bill.

By definition, 1 kilowatt-hour is the energy consumed when an appliance with a power rating of 1000 Watts is used for exactly 1 hour Science, Electricity, p.191. To understand the magnitude of this unit in terms of SI units, we can perform a simple conversion:

• 1 kW h = 1000 Watts × 3600 seconds
• 1 kW h = 3,600,000 Joules (or 3.6 × 10⁶ J) Science, Electricity, p.192.

Another critical concept for competitive exams is the Power Rating. Appliances are rated for a specific voltage (e.g., 220V in India). If the current (I) flowing through a device changes, the power (P) it consumes changes drastically because P is proportional to the square of the current (I²) Science, Electricity, p.189. For example, if the current drops by a small percentage, the power output drops by approximately double 그 percentage (ΔP/P ≈ 2 × ΔI/I). This is why even a slight dip in current can lead to a noticeable dimming of an electric bulb.

From a socio-economic perspective, the per capita consumption of electricity (measured in kWh) is a vital indicator of a nation's development. Currently, India’s average consumption (approx. 350 kWh) lags significantly behind the global average (1000 kWh) and developed nations like the USA (7000 kWh) Geography of India, Energy Resources, p.17.

Sources: Science (NCERT 2025 ed.), Electricity, p.191; Science (NCERT 2025 ed.), Electricity, p.192; Science (NCERT 2025 ed.), Electricity, p.189; Geography of India (Majid Husain, 9th ed.), Energy Resources, p.17

6. Interlinking Power, Current, and Resistance (exam-level)

7. Calculating Percentage Changes in Physics Formulas (exam-level)

In physics, especially when dealing with electricity, we often encounter formulas where one variable is raised to a power. A classic example is Joule’s Law of Heating, which states that the power (P) dissipated as heat in a resistor is proportional to the square of the current (I) passing through it, expressed as P = I²R. Understanding how a percentage change in one variable affects the other is a vital skill for solving exam-level problems efficiently.

When a variable is squared, any small percentage change in that variable results in approximately double that percentage change in the result. This is rooted in differential calculus: if y = xⁿ, then the relative change Δy/y is approximately n × (Δx/x). For our power formula, since the exponent of current (I) is 2, a 1% decrease in current leads to a 2% decrease in power output (Science, Chapter 11: Electricity, p.189). This approximation is incredibly useful for the quick mental math required during competitive exams.

However, precision matters for larger changes. If the current drops by 1%, the new current is 0.99I. Squaring this gives (0.99)²I²R, which equals 0.9801I²R. This represents a 1.99% decrease. While 2% is a near-perfect approximation for a 1% change, as the percentage change grows larger (e.g., a 20% change), the gap between the approximation and the exact value widens. In most UPSC-style physics problems, the linear approximation (multiplying by the exponent) is the intended shortcut for small variations.

Sources: Science, Chapter 11: Electricity, p.189

8. Solving the Original PYQ (exam-level)

To solve this question, you need to synthesize your knowledge of Joule’s Law of Heating and the mathematical relationship between power and current. As you learned in the basics of electricity, the power (P) dissipated in a resistor is given by the formula P = I²R. In the context of an electric bulb, the resistance (R) is considered a constant property of the filament. This means that power is directly proportional to the square of the current. This "square" relationship is the most critical building block here, as it dictates that any change in current will have an amplified effect on the power output.

As your coach, I want you to use a mental shortcut for small percentage changes: when a variable is squared, the percentage change in the result is approximately twice the percentage change in the base variable. Since the current drops by 1%, the power will decrease by approximately 2 × 1% = 2 per cent. If you prefer the exact calculation, a 1% drop means the new current is 0.99I. Squaring this gives (0.99)² = 0.9801, which represents a 1.99% decrease. Rounding this for a quick UPSC response leads us directly to Option (C). This demonstrates how a firm grasp of proportionalities allows you to bypass complex arithmetic during the exam.

UPSC often includes Option (B) 1 per cent as a "linear trap" for students who forget the power is proportional to the square of the current, rather than the current itself. Option (A) 0.5 per cent is a trap for those who might confuse the square relationship with a square root relationship. Understanding that the exponent in P = I²R acts as a multiplier for small percentage changes will help you avoid these common pitfalls and identify the correct relationship instantly. Science, class X (NCERT 2025 ed.)