The figure shows current in a part of electrical network. What is the value of current I ?

1. Fundamentals of Electric Current and Charge (basic)

To understand electricity, we must start with the most fundamental building block: Electric Charge (Q). Charge is an intrinsic property of matter, much like mass. In the context of a circuit, we focus on electrons, which carry a negative charge. When these charges are set in motion—typically by a battery or a cell—they create what we call an Electric Current (I). You can think of current as the rate at which charge flows through a specific cross-section of a conductor. Mathematically, this is expressed as I = Q/t, where t is the time in seconds. The SI unit for charge is the Coulomb (C), while current is measured in Amperes (A), named after André-Marie Ampère Science, Class X (NCERT 2025 ed.), Chapter 11, p.192.

One of the most important (and sometimes confusing) aspects of current is its direction. Historically, electricity was discovered before the electron was known. Scientists assumed that current was the flow of positive charges. Consequently, conventional current is defined as flowing from the positive terminal to the negative terminal of a battery. However, we now know that in metallic wires, it is actually the negatively charged electrons that move. These electrons flow in the opposite direction—from negative to positive. As a student of science, you must remember that the direction of electric current is always taken as opposite to the direction of the flow of electrons Science, Class X (NCERT 2025 ed.), Chapter 11, p.171.

Finally, we must consider how current behaves when it encounters a junction or a "node" in a circuit. Because charge is conserved—meaning it cannot be created or destroyed—the total charge entering a point must equal the total charge leaving it. This leads to a crucial rule: the sum of currents entering a junction is equal to the sum of currents leaving it. If 2A enters a fork in the road and 1A goes left, exactly 1A must go right. This principle of Conservation of Charge is the bedrock of circuit analysis and ensures that the flow remains continuous throughout the system Science, Class X (NCERT 2025 ed.), Chapter 11, p.171.

Sources: Science, class X (NCERT 2025 ed.), Chapter 11: Electricity, p.171; Science, class X (NCERT 2025 ed.), Chapter 11: Electricity, p.192

2. Electric Potential and Potential Difference (basic)

To understand electricity, we must first understand what makes charges move. Imagine water in a perfectly level pipe; it stays still. But if you raise one end of the pipe, creating a difference in pressure, the water flows. In a circuit, electric potential is that "pressure." Electrons do not move on their own; they require a difference in electric pressure, known as the Potential Difference, to flow from one point to another.

In formal terms, the potential difference (V) between two points in an electric circuit is defined as the work done (W) to move a unit charge (Q) from one point to the other. We express this mathematically as:

V = W / Q

The SI unit of potential difference is the Volt (V). By definition, 1 Volt is the potential difference between two points when 1 Joule of work is done to move a charge of 1 Coulomb from one point to the other Science, Chapter 11, p. 173. This "push" is usually provided by a chemical cell or a battery, which uses internal chemical energy to maintain this potential difference across the terminals of a circuit.

When we want to measure this potential difference in a real-world circuit, we use an instrument called a voltmeter. Crucially, a voltmeter is always connected in parallel across the points between which the potential difference is to be measured Science, Chapter 11, p. 185. This allows the device to measure the energy change between those two specific points without becoming a bottleneck for the main current flow.

Sources: Science, Chapter 11: Electricity, p.173; Science, Chapter 11: Electricity, p.185

3. Ohm's Law and the Concept of Resistance (basic)

Imagine trying to push water through a pipe. The pressure you apply is like Potential Difference (V), and the flow of water is the Current (I). In 1827, Georg Simon Ohm discovered that for most metallic conductors, these two are directly proportional: if you double the voltage, the current doubles too. This relationship is famously known as Ohm’s Law, expressed as V = IR.

Here, Resistance (R) is the proportionality constant. Think of it as the 'friction' the conductor offers to the flowing electrons. The SI unit of resistance is the Ohm (Ω). According to Ohm's law, if the resistance of a component is doubled while the voltage remains constant, the current will drop to exactly half its original value Science, class X (NCERT 2025 ed.), Electricity, p.181. This is why we use resistors to control current levels in delicate electronic gadgets.

Resistance isn't a fixed property of a material; it depends on the physical dimensions of the conductor. As per Science, class X (NCERT 2025 ed.), Electricity, p.178, the resistance of a uniform metallic conductor is:

• Directly proportional to its length (l): A longer wire offers more obstacles to electrons.
• Inversely proportional to its area of cross-section (A): A thicker wire allows current to flow more easily, much like a wider highway allows more cars to pass.

Mathematically, we combine these to get R = ρ (l/A), where ρ (rho) is the electrical resistivity. Unlike resistance, resistivity is an intrinsic property of the material itself. For example, metals and alloys have low resistivity (10⁻⁸ Ωm to 10⁻⁶ Ωm), while insulators like rubber have incredibly high resistivity (10¹² to 10¹⁷ Ωm).

Sources: Science, class X (NCERT 2025 ed.), Chapter 11: Electricity, p.178; Science, class X (NCERT 2025 ed.), Chapter 11: Electricity, p.181

4. Electric Power and Heating Effects (intermediate)

When an electric current flows through a conductor, it isn't just a simple movement of charges; it is a process of energy transformation. As electrons navigate through a resistor, they collide with atoms, transferring some of their kinetic energy. This energy appears as heat. This phenomenon, known as the heating effect of electric current, is quantified by Joule’s Law of Heating. According to this law, the heat produced (H) is directly proportional to the square of the current (I²), the resistance (R), and the time (t) for which the current flows: H = I²Rt Science, Chapter 11, p. 189. This heat is an "inevitable consequence" of current in any circuit, and while it leads to energy loss in transmission lines, we harness it deliberately in devices like electric irons, toasters, and water heaters Science, Chapter 11, p. 190.

Moving from the total heat produced to the rate at which this happens brings us to Electric Power (P). Power is defined as the rate at which electrical energy is consumed or dissipated in a circuit. In its most fundamental form, Power is the product of potential difference (V) and current (I): P = VI. By applying Ohm’s Law (V = IR), we can derive two other highly useful expressions for power:

The SI unit of power is the Watt (W), representing 1 Joule of energy consumed per second Science, Chapter 11, p. 191. In our daily lives, however, the Watt is too small a unit. We use the Kilowatt-hour (kWh), which is a unit of energy (Power × Time), commonly referred to as a "unit" on electricity bills. For perspective, 1 kWh equals 3.6 million Joules. Understanding these relationships is vital because it explains why higher resistance in a parallel circuit (like a low-wattage bulb) actually results in less power consumption, whereas in a series circuit, it would lead to more heat dissipation.

Sources: Science, Chapter 11: Electricity, p.189; Science, Chapter 11: Electricity, p.190; Science, Chapter 11: Electricity, p.191

5. Current Distribution in Series and Parallel Circuits (intermediate)

In the study of electricity, understanding how current behaves as it moves through different configurations is fundamental. In a series circuit, there is only one path for the flow of electrons. Imagine a single-lane road: every car that enters must pass through every point on that road. Consequently, the current remains constant at every point in a series combination. Whether you measure the current before a resistor, between two resistors, or after the last one, the ammeter reading will be identical. This is because charge cannot vanish or accumulate along a single path. As noted in Science, Class X (NCERT 2025 ed.), Chapter 11: Electricity, p.187, in a series circuit, the current is constant throughout the electric circuit.

When we move to parallel circuits, the behavior changes significantly. Here, the circuit offers multiple paths (branches) for the current. At a junction (or node), the total current entering must equal the total current leaving. This is known as Kirchhoff’s Current Law (KCL), which is a direct consequence of the Law of Conservation of Charge. If a total current (I) reaches a junction, it splits into branches (I₁, I₂, I₃, etc.) such that I = I₁ + I₂ + I₃. The amount of current that enters each branch depends on the resistance of that specific path; according to Ohm’s Law (I = V/R), a path with higher resistance will draw less current, while a path with lower resistance will draw more. This relationship is observed in experimental setups where the total current is the sum of separate currents through each branch Science, Class X (NCERT 2025 ed.), Chapter 11: Electricity, p.186.

Sources: Science, Class X (NCERT 2025 ed.), Chapter 11: Electricity, p.186-187

6. Kirchhoff's Current Law (KCL): Nodal Analysis (exam-level)

At the heart of analyzing any complex electrical network lies Kirchhoff’s Current Law (KCL), often referred to as the Junction Rule. This principle is a direct consequence of the Law of Conservation of Charge. Just as water flowing through a pipe doesn't simply vanish at a T-junction, electric charge cannot be created or destroyed at a point in a circuit. In a steady-state circuit, charge does not accumulate at a junction; whatever flows in must flow out.

A node (or junction) is any point in a circuit where three or more conductors meet. KCL states that the algebraic sum of currents entering a node is exactly equal to the sum of currents leaving it. Mathematically, this is expressed as ΣI_in = ΣI_out. When we observe a parallel combination of resistors, we see this law in action: the total current I entering the combination is distributed among the various branches, such that I = I₁ + I₂ + I₃ Science, Class X, Electricity, p. 186. This ensures that the total flow of electrons remains consistent throughout the network.

To master Nodal Analysis, you must treat each junction as a checkpoint. Imagine a network where a 5A current hits a junction and splits into two paths. If you measure 2A in one path, KCL dictates that the remaining 3A must be in the other. This isn't just a rule of thumb; it is grounded in the fact that while charges can be static when not in a circuit Science, Class VIII, Exploring Forces, p. 70, once they are in motion (current), they must follow a continuous path. By labeling the currents entering a node as positive and those leaving as negative, the sum of all currents at that node will always be zero (ΣI = 0).

Sources: Science, Class X, Electricity, p.186; Science, Class VIII, Exploring Forces, p.70

7. Solving the Original PYQ (exam-level)

This question is a textbook application of Kirchhoff’s Current Law (KCL), which you recently studied as a direct consequence of the law of conservation of charge. As established in Science, class X (NCERT 2025 ed.), current does not simply vanish; the total magnitude entering a junction must exactly equal the total magnitude leaving it. In this network, you are essentially tracking the "flow" of charge through sequential nodes. The fundamental building block here is understanding that at every intersection, you must perform a net balance to ensure the electrical continuity of the circuit.

To arrive at the solution, let’s walk through the junctions like a coach tracing the path. At the first node, a 2A current enters and splits, leaving 1A to flow forward. At the next junction, this 1A meets a branch where 0.8A exits, leaving 0.2A to continue. Finally, at the node involving current I, we observe that if 0.3A is the total entering current and 0.2A is already accounted for in a parallel branch, the remaining current I must be $0.3A - 0.2A = 0.1A$. Therefore, the correct answer is (B) 0.1 A. Always trace the arrows carefully, as the direction defines whether you are adding to the pool or subtracting from it.

UPSC often designs options to exploit common calculation errors. For example, 0.5 A (Option D) is a classic trap for students who add the branch currents (0.2 + 0.3) instead of recognizing the division of flow. Similarly, 0.2 A (Option A) might tempt someone who stops their analysis one node too early. To succeed in these questions, avoid the urge to mental-math the whole figure at once; instead, isolate each junction and verify the conservation at every step to avoid these logical pitfalls.