A 100 W electric bulb is used for 10 hours a day. How many units of electrical energy are consumed by the bulb in 3 days? (1 unit = 1 kWh)

1. Fundamentals of Electric Current, Voltage, and Resistance (basic)

To understand electricity, we must first look at the tiny particles called electrons. Electric current is essentially a stream of these electrons moving through a conductor, like a copper wire. While electrons actually move from the negative terminal to the positive, by historical convention, we say the current flows in the opposite direction—from positive to negative Science, Class X (NCERT 2025 ed.), Chapter 11, p.192. The SI unit for current is the Ampere (A).

But why do these electrons move at all? They need a "push" or a difference in pressure. This is what we call Potential Difference (or Voltage). It is defined as the work done to move a unit charge from one point to another in a circuit Science, Class X (NCERT 2025 ed.), Chapter 11, p.173. We use a cell or a battery to create this potential difference, measured in Volts (V). Think of it like water in a pipe: voltage is the water pressure, and current is the flow rate of the water itself.

Finally, every material offers some degree of opposition to this flow, which we call Resistance (R). It is the property of a conductor to resist the flow of charges through it Science, Class X (NCERT 2025 ed.), Chapter 11, p.176. The relationship between these three is governed by Ohm’s Law, which states that the potential difference across a conductor is directly proportional to the current flowing through it (V = IR), provided the temperature remains constant. Resistance is measured in Ohms (Ω).

Concept	Definition	SI Unit
Current (I)	The rate of flow of electric charge.	Ampere (A)
Voltage (V)	Work done per unit charge (the "push").	Volt (V)
Resistance (R)	The opposition to the flow of current.	Ohm (Ω)

Sources: Science, Class X (NCERT 2025 ed.), Chapter 11: Electricity, p.173; Science, Class X (NCERT 2025 ed.), Chapter 11: Electricity, p.176; Science, Class X (NCERT 2025 ed.), Chapter 11: Electricity, p.192

2. Electric Power and Joule's Law of Heating (intermediate)

When electric current flows through a conductor, it encounters resistance—think of it as internal friction. As electrons move through the material, they collide with atoms, transferring some of their kinetic energy. This energy manifests as heat, a phenomenon known as the heating effect of electric current Science, Class VIII, Electricity: Magnetic and Heating Effects, p.53. In a purely resistive circuit, the entire energy supplied by the source is dissipated as heat Science, Class X, Electricity, p.188. While this can be a waste in devices like fans or computers, it is the backbone of useful appliances like electric irons, kettles, and toasters Science, Class X, Electricity, p.190.

To quantify this heat, we use Joule’s Law of Heating. It states that the heat (H) produced in a resistor is directly proportional to:

• 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.

Mathematically, this is expressed as H = I²Rt. This law explains why high-power appliances require thicker wires (to handle higher current without melting) and why leaving a device on for longer produces more heat.

Electric Power (P) is the rate at which electrical energy is consumed or dissipated in a circuit. We calculate it using the formula P = VI Science, Class X, Electricity, p.191. By applying Ohm’s Law (V = IR), we can derive two other very useful forms for power:

Formula	Context
P = I²R	Used when components are in series (constant current).
P = V²/R	Used when components are in parallel (constant voltage, like home wiring).

In the scientific community, power is measured in Watts (W), where 1 W = 1 Volt × 1 Ampere. However, for commercial billing, we use the Kilowatt-hour (kWh), which we commonly call a "unit" of electricity.

Sources: Science, Class VIII (NCERT 2025 ed.), Electricity: Magnetic and Heating Effects, p.53; Science, Class X (NCERT 2025 ed.), Chapter 11: Electricity, p.188, 190, 191

3. Domestic Electrical Circuits and Safety Devices (basic)

In our homes, electricity is supplied through a complex network of wires designed to be both efficient and safe. This system typically involves three types of wires: the Live wire (usually with red insulation), the Neutral wire (black insulation), and the Earth wire (green insulation). In India, the potential difference between the live and neutral wires is maintained at 220 V. While the live and neutral wires carry the current to our appliances, the earth wire is a safety feature connected to a metal plate deep in the earth near the house Science, Class X (NCERT 2025 ed.), Chapter 12, p.205.

One of the most critical design choices in domestic wiring is the use of parallel circuits. Unlike a series circuit—where if one component fails, the entire circuit breaks—a parallel circuit ensures that each appliance can be turned on or off independently using its own switch. More importantly, connecting appliances in parallel ensures that each one receives the full 220 V potential difference, allowing them to operate at their rated power Science, Class X (NCERT 2025 ed.), Chapter 11, p.187.

Feature	Series Connection	Parallel Connection (Domestic)
Voltage	Divided among components	Constant (220V) for all
Independence	One failure stops everything	Appliances work independently
Current	Same through all devices	Divided based on appliance need

To protect these circuits from damage caused by overloading or short-circuiting, we use safety devices like the Electric Fuse. A fuse is a thin wire made of an alloy with a low melting point, placed in series with the live wire. If the current exceeds a specific limit (e.g., 5 A or 15 A), the wire heats up due to Joule heating and melts, instantly breaking the circuit to prevent fire or appliance damage Science, Class X (NCERT 2025 ed.), Chapter 11, p.190. Similarly, Earthing is used for appliances with metallic bodies (like irons or refrigerators); it provides a low-resistance path for any leaked current to flow into the ground, protecting the user from severe electric shocks Science, Class X (NCERT 2025 ed.), Chapter 12, p.206.

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.187, 190

4. Energy Sector Context: Power Generation and Net Metering (intermediate)

To master the energy sector, we must first understand how we measure what we consume. While Power (measured in Watts or kW) tells us the rate at which energy is used, Electrical Energy is the total work done over a period of time. The standard commercial unit for billing is the kilowatt-hour (kWh), which is colloquially called a 'unit'. One 'unit' represents the energy consumed by a 1000-watt appliance running for exactly one hour Science, class X (NCERT 2025 ed.), Chapter 11, p. 191. For instance, if you use a 100 W bulb for 10 hours, the calculation is: 0.1 kW × 10 h = 1 kWh (or 1 unit). Over three days, this simple bulb would consume 3 units of electricity.
As India moves toward a Smart City model, providing reliable physical infrastructure like power supply is a core pillar of development Indian Economy, Vivek Singh (7th ed.), Infrastructure and Investment Models, p. 435. A major shift in this infrastructure is the transition from centralized coal plants to decentralized Renewable Energy. Solar energy is a leader here, as Photovoltaic (PV) cells convert sunlight directly into electricity, proving significantly more effective and environment-friendly than coal-based plants INDIA PEOPLE AND ECONOMY (NCERT 2025 ed.), Mineral and Energy Resources, p. 61. Massive projects like the Shakti Sthala solar park in Karnataka (2,050 MW) showcase India's scaling capacity Indian Economy, Nitin Singhania (2nd ed.), Infrastructure, p. 449.
This brings us to the concept of Net Metering. In a traditional system, you only consume power from the grid. However, with rooftop solar PV systems, consumers become 'prosumers'—they both produce and consume. Net metering is a billing mechanism that credits solar energy system owners for the electricity they add to the grid. If you generate more than you use, the meter literally runs backward, and you are only billed for the 'net' energy consumed. This integrates perfectly with Waste-to-Energy initiatives, which aim to recover power from municipal and industrial waste, further diversifying our energy grid Environment, Shankar IAS Academy (10th ed.), Renewable Energy, p. 294.

Technology	Mechanism	Primary Use
Solar Photovoltaic (PV)	Direct conversion of sunlight to electricity via cells.	Residential rooftops, large solar parks.
Solar Thermal	Using sun's heat to produce steam for turbines or heating.	Industrial heaters, crop dryers, cookers.

Sources: Science, class X (NCERT 2025 ed.), Chapter 11: Electricity, p.191-192; Indian Economy, Vivek Singh (7th ed. 2023-24), Infrastructure and Investment Models, p.435; INDIA PEOPLE AND ECONOMY (NCERT 2025 ed.), Mineral and Energy Resources, p.61; Indian Economy, Nitin Singhania (ed 2nd 2021-22), Infrastructure, p.449; Environment, Shankar IAS Academy (ed 10th), Renewable Energy, p.294

5. The Commercial Unit of Electrical Energy (kWh) (exam-level)

In our previous discussions, we established that Electric Power is the rate at which electrical energy is consumed. However, when we transition from the laboratory to the real world—specifically to our electricity bills—the standard SI unit of energy, the Joule (J), becomes impractically small. Imagine trying to measure the distance between Delhi and Mumbai in millimeters! To solve this, we use the Commercial Unit of Electrical Energy, known as the kilowatt-hour (kWh), or simply a 'unit'.

To understand this from first principles, remember that Energy = Power × Time. While 1 Watt-hour (Wh) is the energy consumed when 1 Watt of power is used for 1 hour, the commercial world operates on a scale 1,000 times larger. Therefore, 1 kilowatt-hour is the energy consumed by an electrical appliance with a power rating of 1000 Watts (1 kW) when it is used for one hour Science, Chapter 11: Electricity, p.191. In administrative and economic contexts, this 1 kWh is the standard 'unit' used to calculate power tariffs for different energy sources, such as solar, wind, or thermal power Indian Economy, Infrastructure and Investment Models, p.431.

It is crucial to know how to convert these commercial units back into the standard Joules for scientific calculations. Since 1 kW = 1000 W and 1 hour = 3600 seconds, we can derive the relationship as follows:

• 1 kWh = 1000 Watts × 3600 seconds
• 1 kWh = 3,600,000 Watt-seconds
• 1 kWh = 3.6 × 10⁶ Joules Science, Chapter 11: Electricity, p.192

From a developmental perspective, the per capita consumption of electricity is a major indicator of a nation's growth. For instance, India's per capita consumption is approximately 350 kWh, which is significantly lower than the global average of 1000 kWh, highlighting the energy infrastructure challenges the country aims to address Geography of India, Energy Resources, p.30.

Sources: Science, Chapter 11: Electricity, p.191-192; Indian Economy, Infrastructure and Investment Models, p.431; Geography of India, Energy Resources, p.30

6. Solving the Original PYQ (exam-level)

Now that you have mastered the fundamental definitions of Electric Power and its relationship with time, this question brings those building blocks together. The core concept here is the conversion of Power (Watts) into Commercial Energy (kWh). As you learned in the previous modules, 1 unit is exactly 1 kilowatt-hour. To tackle this, you must apply the principle that Electrical Energy is the product of power and time, while ensuring your units are mathematically compatible—specifically converting Watts to Kilowatts—before your final calculation.

Let's walk through the logic as a seasoned aspirant would: first, convert the 100 W bulb to kilowatts by dividing by 1,000, which gives us 0.1 kW. Since the bulb operates for 10 hours a day, the daily consumption is 0.1 kW × 10 h = 1 kWh (or 1 unit). However, the question asks for the consumption over 3 days, so the total becomes 1 unit/day × 3 days = 3 units. This systematic approach, as detailed in Science, class X (NCERT 2025 ed.), ensures you don't miss the multi-day component of the question. Therefore, the correct answer is (A) 3:00.

UPSC frequently includes distractors to catch students who perform incomplete calculations. For example, a student might correctly calculate 1 unit for a single day but forget to multiply by the 3-day duration, or they might fail the decimal conversion from Watts to Kilowatts. Options (B), (C), and (D) are designed to look plausible if you mistakenly use 24-hour cycles or incorrect power-to-energy ratios. By sticking strictly to the Energy = Power × Time formula and isolating the time duration clearly, you can easily bypass these common traps.