Ohm’s law does not apply to which of the following ?

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

To understand electricity, we must first visualize what is happening inside a wire. Electric current is defined as the rate of flow of electric charges, specifically electrons, through a conductor. Think of it like water flowing through a pipe; the more water passing through a cross-section per second, the higher the "current." In an electric circuit, the SI unit for current is the Ampere (A). A fascinating historical quirk to remember is that conventionally, we say current flows from the positive terminal to the negative terminal, which is exactly opposite to the actual direction of electron flow Science, Chapter 11, p.192.

But what makes these electrons move in the first place? They require a push, which we call Electric Potential Difference (often just called voltage). Science defines this as the amount of work done to move a unit charge from one point to another in a circuit. Without this difference in "electrical pressure," electrons would simply sit still. We measure this in Volts (V), named after Alessandro Volta. Quantitatively, it is expressed as:

V = W / Q

Where V is potential difference, W is work done (in Joules), and Q is the quantity of charge (in Coulombs) Science, Chapter 11, p.173. One Volt is precisely the potential difference needed when 1 Joule of work is done to move 1 Coulomb of charge.

In a practical circuit, a cell or battery acts as the pump that maintains this potential difference across the terminals. As long as the battery maintains this difference, current continues to flow. However, no path is perfectly clear; every conductor offers some resistance, a property that naturally opposes the flow of electrons and helps control the magnitude of the current Science, Chapter 11, p.192.

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

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

At the heart of understanding how electricity behaves in a circuit is Ohm’s Law. It describes a simple yet profound relationship: the potential difference (voltage, V) across the ends of a metallic wire is directly proportional to the current (I) flowing through it. Mathematically, this is expressed as V ∝ I, or more commonly, V = IR. Here, R represents Resistance, a constant for a given conductor at a specific temperature Science, Class X (NCERT 2025 ed.), Chapter 11: Electricity, p.176. Resistance is essentially the property of a material to oppose or "resist" the flow of electric charges. The SI unit for resistance is the ohm (Ω); one ohm is defined as the resistance of a conductor such that a potential difference of 1 Volt results in a current of 1 Ampere Science, Class X (NCERT 2025 ed.), Chapter 11: Electricity, p.192.

It is crucial to remember that Ohm’s Law is not a universal law for all materials under all conditions. It holds true only if physical conditions, specifically temperature, remain constant. When a conductor follows this linear relationship where the V-I graph is a straight line passing through the origin, we call it an Ohmic conductor. However, many modern electronic components like semiconductors (diodes and transistors) are non-ohmic. In these materials, the relationship between voltage and current is non-linear, meaning their resistance changes depending on the amount of voltage applied or the current flowing through them.

The resistance of a wire isn't just a random number; it depends on the physical characteristics of the material. Specifically, the resistance (R) of a uniform metallic conductor is directly proportional to its length (l) and inversely proportional to its area of cross-section (A) Science, Class X (NCERT 2025 ed.), Chapter 11: Electricity, p.192. This means a longer wire offers more resistance, while a thicker wire (larger cross-section) offers less, much like how water flows more easily through a wide pipe than a narrow one.

Factor	Effect on Resistance (R)	Logic
Length (l)	Increases	Electrons collide with more atoms over a longer path.
Area (A)	Decreases	A wider "pathway" allows more charges to flow simultaneously.
Temperature	Increases (for metals)	Atoms vibrate more, making it harder for electrons to pass through.

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)

Resistance is not a fixed attribute of a material; rather, it is a behavior that depends on how the material is shaped and what it is made of. To understand this, imagine water flowing through a pipe: a longer pipe offers more surface for friction, while a wider pipe allows more water to pass through at once. Similarly, the resistance (R) of a conductor is directly proportional to its length (l) and inversely proportional to its area of cross-section (A) Science, Chapter 11, p.178. This means if you double the length of a wire, you double its resistance; but if you double its thickness (cross-sectional area), you halve its resistance. While resistance depends on the geometry (shape) of the object, resistivity (ρ) is an intrinsic property of the material itself. It tells us how strongly a material opposes current regardless of its shape. The relationship is expressed by the formula: R = ρ l/A. Metals like silver and copper have very low resistivity (10⁻⁸ Ω m), making them ideal for transmission lines, while insulators like glass have extremely high resistivity Science, Chapter 11, p.179. Interestingly, alloys (like nichrome) generally have higher resistivity than their constituent pure metals and do not oxidize easily at high temperatures, which is why they are used in heating elements like toasters and electric irons Science, Chapter 11, p.179.

Feature	Resistance (R)	Resistivity (ρ)
Definition	Opposition to current flow in a specific object.	The inherent resistance of a material type.
Depends on	Length, Area, Material, and Temperature.	Nature of Material and Temperature only.
SI Unit	Ohm (Ω)	Ohm-meter (Ω m)

Temperature also plays a critical role. For most pure metals, resistance and resistivity increase as the temperature rises. This happens because higher temperatures cause the atoms in the conductor to vibrate more vigorously, leading to more frequent collisions with the flowing electrons, thereby hindering their movement Science, Chapter 11, p.179.

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

4. Heating Effects and Electrical Power (intermediate)

When an electric current flows through a conductor, it isn't a frictionless journey. Electrons constantly collide with the atoms of the conductor, transferring a portion of their kinetic energy. This energy manifests as heat. While we often try to minimize this loss in transmission lines, it is the very principle that makes your morning toast possible. This phenomenon is known as the heating effect of electric current, and it is governed by Joule’s Law of Heating.

According to this law, the heat produced (H) in a resistor is directly proportional to three factors: the square of the current (I²), the resistance (R), and the time (t) for which the current flows. Mathematically, this is expressed as H = I²Rt Science, Class X (NCERT 2025 ed.), Chapter 11, p.189. This means if you double the current passing through a wire, the heat generated doesn't just double—it quadruples! This exponential relationship is why high-power appliances require thicker wires to handle the resulting thermal load without melting.

Electrical Power (P) is the rate at which this electrical energy is consumed or dissipated in a circuit. In simpler terms, it tells us how fast work is being done. We calculate it using the relationship P = VI. By applying Ohm’s law (V = IR), we can derive two other incredibly useful forms of the power equation depending on which variables we know:

Formula	Best Used When...
P = VI	You know the voltage and the measured current.
P = I²R	You know the current and the resistance (common for series circuits).
P = V²/R	You know the voltage and the resistance (common for parallel/home circuits).

In practical applications, we see two sides of this coin. In devices like electric irons or water heaters, we maximize the heating effect using high-resistance alloys like Nichrome. In incandescent bulbs, the filament (usually Tungsten) is heated to such an extreme temperature that it begins to glow and emit light Science, Class X (NCERT 2025 ed.), Chapter 11, p.190. Conversely, in computers and smartphones, this heat is an "inevitable consequence" that we must actively manage with fans or heat sinks to prevent damage.

Sources: Science, Class X (NCERT 2025 ed.), Chapter 11: Electricity, p.189; Science, Class X (NCERT 2025 ed.), Chapter 11: Electricity, p.190; Science, Class X (NCERT 2025 ed.), Chapter 11: Electricity, p.191

5. Alternating Current (AC) and Impedance (exam-level)

In our previous steps, we looked at how current flows through a conductor. When we deal with Alternating Current (AC), the situation becomes more dynamic. Unlike Direct Current (DC), where electrons flow in a single direction, AC periodically reverses its direction. In India, our domestic power supply is AC with a potential difference of 220 V and a frequency of 50 Hz, meaning the direction of current changes 100 times per second Science, Magnetic Effects of Electric Current, p.206.

While we use the term Resistance (R) to describe the opposition to current in a simple DC circuit, AC circuits often involve more complex components like coils (inductors) and capacitors. These components don't just resist flow; they respond to the changing frequency of the current. To account for this total opposition, we use the term Impedance (Z). Think of Impedance as the "big brother" of Resistance—it includes the standard resistance from atoms obstructing electrons Science, Electricity, p.177, but also adds the effects of the components' reactions to the alternating nature of the current.

In a domestic setting, this power reaches us through a three-wire system: the Live wire (red insulation), the Neutral wire (black insulation), and the Earth wire (green insulation). The Earth wire is a safety measure, connected to a metallic body deep in the earth to prevent shocks Science, Magnetic Effects of Electric Current, p.206. Understanding impedance is crucial because while Ohm’s Law (V = IR) works perfectly for DC resistors, in AC circuits, we must use the generalized version: V = IZ.

Feature	Resistance (R)	Impedance (Z)
Application	Direct Current (DC) and AC	Alternating Current (AC)
Components	Only Resistors	Resistors, Inductors, and Capacitors
Frequency	Independent of frequency	Changes with the frequency of AC

Sources: Science, Magnetic Effects of Electric Current, p.206; Science, Electricity, p.177; Science, Electricity, p.192

6. Ohmic vs. Non-Ohmic Materials (exam-level)

To understand the behavior of electrical circuits, we must distinguish between materials based on how they respond to electrical pressure (voltage). At the heart of this distinction is Ohm’s Law, which states that the potential difference (V) across a conductor is directly proportional to the current (I) flowing through it, provided physical conditions like temperature remain constant Science, Chapter 11, p.192.

Ohmic materials are those that strictly follow this linear relationship. For these materials, if you double the voltage, the current doubles, meaning the resistance (R) remains constant. Most metals, such as copper, silver, and aluminum, behave as ohmic conductors under normal operating conditions. If you were to plot their behavior on a graph (a V-I graph), you would see a perfectly straight line passing through the origin. The slope of this line represents the resistance of the material.

However, many modern electronic components are Non-Ohmic. In these materials, the ratio of voltage to current is not constant; the resistance changes as the current or voltage changes. This non-linearity is often due to the internal physics of the material or changes in environmental factors like heat. For instance, as a filament lamp gets hotter, its resistance increases significantly, causing its V-I graph to curve rather than stay straight. In the world of advanced electronics, semiconductors like diodes and transistors are inherently non-ohmic because they are designed to control the flow of current in specific, non-linear ways.

Feature	Ohmic Materials	Non-Ohmic Materials
V-I Relationship	Linear (Straight line)	Non-linear (Curved line)
Resistance (R)	Constant	Variable
Examples	Copper, Iron, Nichrome wire	Diodes, Transistors, Filament lamps
Governing Rule	Follows Ohm's Law	Violates Ohm's Law proportionality

Sources: Science (NCERT 2025 ed.), Chapter 11: Electricity, p.192

7. Physics of Semiconductors (exam-level)

To understand semiconductors, we must first look at the spectrum of electrical conductivity. While conductors like copper and silver allow electricity to flow easily because they have a high density of free electrons, insulators like rubber and ceramics offer such high resistance that current flow is negligible Science, Class X, Chapter 11, p.177. Semiconductors sit in the 'goldilocks zone' between these two. Their unique atomic structure—often visualized through electron-dot structures showing how valence electrons are shared—determines how they carry charge Science, Class X, Chapter 3, p.49. Unlike metals, which have a sea of free electrons, semiconductors require a small 'nudge' of energy (heat or light) to move electrons from a bound state to a conductive state.

The defining characteristic of semiconductors in physics is that they are non-ohmic. Ohm’s Law states that current is directly proportional to voltage (V = IR), provided temperature remains constant Science, Class X, Chapter 11, p.192. However, in devices like diodes and transistors, this linear relationship breaks down. The resistance of a semiconductor is not a fixed number; it varies significantly based on the applied voltage. For instance, a diode may allow no current to flow at low voltages but suddenly 'turn on' and allow massive flow once a specific threshold is crossed. This property allows semiconductors to act as electronic switches, which is the foundational logic of every computer chip.

Another critical distinction is how these materials respond to heat. In a standard metallic conductor, increasing the temperature causes atoms to vibrate more, obstructing electron flow and increasing resistance. In contrast, heating a semiconductor provides the energy needed to liberate more charge carriers (electrons and 'holes'), which actually decreases its resistance. This inverse relationship is why semiconductors are so sensitive to thermal environments. This sensitivity is harnessed in technologies like solar panels, which convert light energy into electrical flow by exciting these charge carriers Science, Class VII, Chapter 3, p.40.

Property	Conductors (e.g., Copper)	Semiconductors (e.g., Silicon)
Ohm's Law	Ohmic (Linear V-I relationship)	Non-Ohmic (Non-linear V-I relationship)
Temp. vs Resistance	Temp ↑ , Resistance ↑	Temp ↑ , Resistance ↓
Charge Carriers	Free Electrons	Electrons and Holes

Sources: Science, Class X, Chapter 11: Electricity, p.177, 192; Science, Class X, Chapter 3: Metals and Non-metals, p.49; Science, Class VII, Chapter 3: Electricity: Circuits and their Components, p.40

8. Solving the Original PYQ (exam-level)

This question effectively synthesizes your understanding of proportionality and the physical properties of matter. To arrive at the correct answer, you must apply the building block of Ohmic vs. Non-Ohmic behavior. Ohm’s Law is predicated on the idea that resistance remains constant; however, in Semiconductors, the flow of charge carriers is non-linear. As you increase voltage in a diode or transistor, the current does not rise at a steady rate, directly violating the V = IR consistency. Therefore, (C) Semiconductors is the correct choice because their internal physics inherently prevents a constant linear relationship.

As an aspirant, you must be wary of the common traps found in the other options. Option (D) is a classic distractor; while temperature changes do affect resistance, a conductor is still considered an Ohmic material whose behavior is simply being modified by external conditions. Similarly, AC circuits (A) do not invalidate the law; they merely require the use of impedance to account for phase shifts. The key takeaway is to distinguish between a law being modified by conditions versus a material whose fundamental nature falls outside the law’s scope, as detailed in Science, class X (NCERT 2025 ed.) and IIT Kanpur SATHEE Physics resources.