How many sixty watt (60 W) bulbs may be safely used in a 240-V supply with 4-ampere fuse?

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

Welcome to your first step in mastering Electricity and Magnetism! To understand how any electrical device works, we must first grasp the three fundamental pillars: Electric Current, Potential Difference (Voltage), and Resistance. Think of electricity like water flowing through a pipe; this analogy helps visualize these abstract concepts beautifully.

Electric Current (I) is essentially a stream of moving charges. In a metallic wire, these charges are electrons. We define current as the rate of flow of electric charge through a cross-section of a conductor. According to Science, Class X (NCERT 2025 ed.), Electricity, p.192, the SI unit of current is the ampere (A). Conventionally, we say current flows from the positive terminal to the negative terminal, which is exactly opposite to the actual direction of electron flow.

But why do these electrons move at all? They need a "push." This push is provided by the Potential Difference (V), often called Voltage. It is defined as the work done to move a unit charge from one point to another in an electric circuit (Science, Class X (NCERT 2025 ed.), Electricity, p.173). We measure this in volts (V). Just as water only flows from a high-pressure area to a low-pressure area, electrons only move when there is a difference in electric potential created by a cell or a battery.

Finally, we have Resistance (R). No conductor is perfect; every material offers some obstruction to the flow of electrons. This property to resist the flow of charges is called resistance, measured in ohms (Ω) (Science, Class X (NCERT 2025 ed.), Electricity, p.192). The relationship between these three is governed by Ohm’s Law, which states that the current through a conductor is directly proportional to the potential difference across its ends (V = IR), provided physical conditions like temperature remain constant (Science, Class X (NCERT 2025 ed.), Electricity, p.176).

Concept	Analogy (Water Pipe)	SI Unit	Formula
Current (I)	Flow rate (liters per second)	Ampere (A)	I = Q/t
Voltage (V)	Water pressure/Pump push	Volt (V)	V = W/Q
Resistance (R)	Pipe narrowness/Obstacles	Ohm (Ω)	R = V/I

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

2. Electric Power and Commercial Units of Energy (basic)

In our daily lives, we use various electrical appliances, from a tiny LED bulb to a heavy-duty air conditioner. But how do we measure the "strength" or the rate at which these devices consume energy? This is where Electric Power comes in. In simple terms, power is the rate of doing work or the rate at which electrical energy is dissipated in a circuit Science, Class X, Electricity, p.191. If a device consumes energy quickly, it has high power; if it consumes energy slowly, it has low power.

Mathematically, electric power (P) is the product of the potential difference (V) across the device and the current (I) flowing through it: P = V × I. The SI unit of power is the Watt (W). One watt is defined as the power consumed by a device that carries 1 Ampere of current when operated at a potential difference of 1 Volt Science, Class X, Electricity, p.191. By applying Ohm’s Law (V = IR), we can also express power in terms of resistance as P = I²R or P = V²/R Science, Class X, Electricity, p.193. These formulas are crucial for engineers when designing circuits to ensure wires don't overheat.

While the Watt is the standard unit, it is quite small for practical utility purposes. Imagine measuring the distance between two cities in millimeters! To handle large amounts of energy, we use the Commercial Unit of Electrical Energy, known as the kilowatt-hour (kWh), often simply called a "unit" on your electricity bill Science, Class X, Electricity, p.192. It represents the energy consumed by a 1000-watt appliance running for exactly one hour.

Unit	Value in Joules	Usage Context
1 Watt-second (Joule)	1 J	Scientific/Small scale
1 kilowatt-hour (kWh)	3.6 × 10⁶ J	Commercial/Household bills

Sources: Science, Class X, Electricity, p.191; Science, Class X, Electricity, p.192; Science, Class X, Electricity, p.193

3. Series and Parallel Circuits in Domestic Wiring (intermediate)

In domestic wiring, the fundamental goal is to ensure that every appliance—be it a small LED bulb or a heavy-duty air conditioner—operates independently and efficiently. To achieve this, we use a parallel circuit layout. Unlike a series circuit where components are connected end-to-end in a single loop, a parallel circuit connects each appliance across the live and neutral wires. This configuration ensures that every device receives the same potential difference, which in our country is standard at 220 V Science, Class X (NCERT 2025 ed.), Magnetic Effects of Electric Current, p.204.

The choice of parallel wiring over series is driven by two critical practicalities. First, in a series circuit, if one component fails or a bulb "blows," the entire circuit is broken and all other appliances stop working. In a parallel circuit, each appliance has its own separate path for current and its own independent ON/OFF switch Science, Class X (NCERT 2025 ed.), Magnetic Effects of Electric Current, p.205. Second, because each branch is connected to the same mains points, the voltage remains constant across every appliance, allowing them to draw the specific amount of current they need to function at their rated power Science, Class X (NCERT 2025 ed.), Electricity, p.185.

However, we must be mindful of overloading. In a parallel setup, as you turn on more appliances, the total current drawn from the mains increases (since the total current is the sum of currents in all branches). If the total current exceeds the safe limit of the wires, it can cause overheating and fire. To prevent this, an electric fuse is always connected in series with the live wire Science, Class X (NCERT 2025 ed.), Magnetic Effects of Electric Current, p.205. The fuse acts as a "sacrificial" link that melts and breaks the circuit if the current becomes dangerously high.

Feature	Series Connection	Parallel (Domestic) Connection
Voltage (V)	Shared/Divided among devices	Constant (Same for all devices)
Independence	If one fails, all fail	Independent operation of devices
Total Current	Same current through all	Sum of individual branch currents

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.205; Science, Class X (NCERT 2025 ed.), Electricity, p.185

4. Safety Mechanisms: Electric Fuse and MCBs (intermediate)

In any domestic electrical circuit, safety mechanisms are essential to prevent disasters like fires or appliance damage. The two primary threats are short-circuiting (when live and neutral wires touch directly due to damaged insulation) and overloading (when too many high-power appliances are used simultaneously). In both cases, the current in the circuit increases abruptly, leading to excessive heat generation as per Joule’s Law of Heating (H = I²Rt), which states that the heat produced is directly proportional to the square of the current Science, Class X (NCERT 2025 ed.), Electricity, p.189.

The Electric Fuse is the traditional guardian of the circuit. It consists of a thin wire made of a metal or alloy with a low melting point (like lead-tin alloy or copper). It is always connected in series with the live wire. If the current exceeds a specific safety limit (the fuse rating), the Joule heating becomes intense enough to melt the fuse wire, thereby breaking the circuit and stopping the flow of electricity before the house wiring can catch fire Science, Class X (NCERT 2025 ed.), Electricity, p.190.

In modern homes, Miniature Circuit Breakers (MCBs) have largely replaced fuses. Unlike a fuse, which must be replaced once it melts, an MCB is a switch that automatically "trips" or turns OFF when the current exceeds the safe limit. They work on either thermal principles (using a bimetallic strip that bends when hot) or electromagnetic principles (using a solenoid that pulls a lever when current is too high). Once the fault is corrected, you simply flip the switch back up to restore power, making them more convenient and precise than traditional fuses.

Feature	Electric Fuse	MCB (Circuit Breaker)
Action	Melts to break the circuit.	Trips (switches off) to break the circuit.
Reusability	Must be replaced after one use.	Can be reset and reused.
Speed	Relatively slower response.	Very fast response to overcurrent.

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

5. Energy Efficiency and Lighting Technology (exam-level)

To understand energy efficiency in lighting, we must first look at how we convert electricity into visible light. Traditional incandescent bulbs operate on the principle of Joule heating. They use a filament made of tungsten, a metal specifically chosen for its exceptionally high melting point (3380°C), which allows it to glow white-hot without melting Science, Class X, p.190. To prevent the filament from burning up, bulbs are filled with chemically inactive gases like nitrogen or argon. However, these bulbs are remarkably inefficient because the majority of the electrical energy is wasted as heat, with only a tiny fraction emitted as light.

Modern Light Emitting Diodes (LEDs) have revolutionized this field. Unlike incandescent bulbs, LEDs do not rely on a heated filament. They are significantly more energy-efficient, consume much less power for the same brightness, and have a far longer lifespan Science, Class VII, p.154. This transition is not just a technological upgrade but a policy priority in India to reduce national energy demand and environmental impact.

When designing or using lighting circuits, safety is maintained by a fuse. A fuse is a safety device with a specific current rating that protects the circuit by breaking the flow if the current becomes too high Science, Class X, p.190. The relationship between power (P), voltage (V), and current (I) is defined by the formula: P = V × I. By knowing the supply voltage and the fuse rating, we can calculate the total wattage a circuit can safely support before the fuse melts.

Feature	Incandescent Bulb	LED Lamp
Mechanism	Thermal radiation (Joule heating)	Electroluminescence
Efficiency	Low (most energy lost as heat)	High (minimal heat loss)
Lifespan	Short	Very Long

Sources: Science, Class X, Electricity, p.190; Science, Class VII, Light: Shadows and Reflections, p.154

6. Load Calculation and Circuit Overloading (intermediate)

Every electrical circuit has a defined "load capacity" determined by its wiring and safety devices. Think of it like a bridge that can only support a certain amount of weight; if you exceed that weight, the structure is compromised. In domestic wiring, appliances are connected in **parallel**, which means each device receives the same supply voltage (usually 220V or 240V in India). As you turn on more appliances, the total current drawn from the source increases because the total resistance of the circuit decreases Science, class X (NCERT 2025 ed.), Electricity, p.187. To calculate the safe limit of a circuit, we use the fundamental power formula: **P = V × I**. Here, **P** is power in Watts, **V** is the supply voltage, and **I** is the current in Amperes. If you know the **Fuse Rating** (the maximum current the circuit can handle), you can determine the maximum power capacity. For example, in a 240V circuit with a 5A fuse, the maximum power is 1200W. If the total power of all active appliances exceeds this value, the circuit is "overloaded." **Overloading** can happen in two primary ways:

• Excessive Load: Connecting too many high-power appliances (like heaters or air conditioners) to a single socket or circuit simultaneously.
• Short-Circuiting: If the insulation of wires is damaged and the live wire touches the neutral wire directly, the resistance drops almost to zero, causing the current to "abruptly increase" to dangerous levels Science, class X (NCERT 2025 ed.), Magnetic Effects of Electric Current, p.205.

To prevent fires or damage, we use an **electric fuse**. This device contains a wire with a low melting point. When the current exceeds the safe limit, **Joule heating** causes the fuse wire to melt, breaking the circuit and stopping the flow of electricity Science-Class VII, NCERT(Revised ed 2025), Electricity: Circuits and their Components, p.27.

Overloading

Short-Circuit

Condition	Cause	Effect on Current
Normal Operation	Load within fuse rating	Stable and safe
Too many appliances or voltage hike	Gradual/Significant increase
Direct contact of live and neutral wires	Abrupt, extreme increase

Sources: Science, class X (NCERT 2025 ed.), Electricity, p.187; Science, class X (NCERT 2025 ed.), Magnetic Effects of Electric Current, p.205; Science-Class VII, NCERT(Revised ed 2025), Electricity: Circuits and their Components, p.27

7. Solving the Original PYQ (exam-level)

Now that you have mastered the fundamentals of electric power and circuit safety, this question serves as the perfect synthesis of those building blocks. In any electrical system, the fuse rating acts as the maximum 'current budget' allowed to flow through the circuit. By applying the Power Law (P = V × I), which you recently studied, you can bridge the gap between the voltage provided by the mains and the safety limit set by the fuse to determine the total 'power capacity' available for your appliances.

To solve this like a seasoned aspirant, think of the fuse as a gatekeeper: it allows a maximum of 4 Amperes. You can approach the reasoning in two ways. Method 1: Calculate the total power capacity of the circuit by multiplying the supply voltage (240V) by the fuse limit (4A), which gives you 960 Watts. Since each bulb consumes 60W, dividing 960 by 60 gives you exactly 16 bulbs. Method 2: Determine the current drawn by a single bulb ($60W / 240V = 0.25A$). To find how many such bulbs fit into a 4A limit, divide 4 by 0.25, which again leads you to (D) 16. Both paths confirm that 16 is the threshold of safety.

UPSC often includes 'distractor' options to catch students who rush. Option (A) 4 is a common trap for those who might see the '4-ampere' figure and assume a 1:1 ratio without calculating power. Options (B) 8 and (C) 12 are designed to catch calculation errors or the use of 110V (common in other countries) instead of the 240V specified. Remember, as discussed in NCERT Class 10 Science, the total current in a parallel home circuit is the sum of currents through each appliance; exceeding 16 bulbs would push the current past 4A, causing the fuse to melt and break the circuit.