📚 Theory Guide

🔌 Ohm's Law

Complete NEB Class 11 theory — from first principles to real-world circuits. Master voltage, current, resistance and everything in between.

⚡ V = IR 📈 V-I Characteristics 🧪 Resistivity ⚖️ Ohmic vs Non-Ohmic 🎓 Viva Questions
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The Foundation of Every Circuit

Every electronic device on Earth — your phone, your laptop, the television in your living room, the streetlights outside — relies on one single relationship to function: Ohm's Law. Discovered by German physicist Georg Simon Ohm in 1827, this law connects voltage, current, and resistance in a beautifully simple equation that unlocks the entire world of electricity.

Think of electricity like water flowing through a pipe. Voltage is the water pressure pushing it forward. Current is how much water actually flows through. And Resistance is how narrow or blocked the pipe is. Ohm's Law tells us exactly how these three things relate — and that relationship holds true in every circuit you will ever encounter, from a simple LED to a rocket engine's control panel.

In your NEB Class 11 practical, you'll build a real circuit, vary the voltage using a rheostat, measure current with an ammeter, and plot a V-I graph that proves this law right in front of your eyes. This guide will make sure you understand every concept deeply — not just for the exam, but for life.

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Historical Fact

Georg Ohm was actually ridiculed when he first published his law — the scientific community called it "too simple to be useful." It took nearly two decades before the world fully recognised its genius. Today, the unit of resistance — the Ohm (Ω) — is named permanently in his honour.

What You'll Master

⚡ The Law

Ohm's Law — Statement & Meaning

Statement: At constant temperature, the electric current flowing through a conductor is directly proportional to the potential difference (voltage) applied across its ends.

Mathematically, I ∝ V at constant temperature. Introducing the constant of proportionality — which we call resistance R — we arrive at the iconic equation:

V = I × R
V = Potential Difference (Volts)  |  I = Current (Amperes)  |  R = Resistance (Ohms, Ω)

This single equation can be rearranged to isolate any one quantity when the other two are known:

I = V / R      R = V / I
Use whichever rearrangement matches the quantity you need to find
🧠

Memory Trick — The OHM Triangle

Draw a triangle with V at the top, I at the bottom-left, and R at the bottom-right. Cover the letter you want to find — the remaining two show the operation. Side by side means multiply; one above the other means divide. Simple and never forgets.


🔬 Derivation

Deriving Ohm's Law from Drift Velocity

Ohm's Law is not just a rule we memorise — it can be proved from the microscopic behaviour of electrons drifting inside a conductor. This is what separates true understanding from surface-level knowledge.

Step-by-Step Derivation

1
Current is defined as charge flowing per unit time. If n = number density of free electrons, e = charge of one electron, A = cross-sectional area, and vd = drift velocity, then: I = n · A · e · vd
2
When a voltage V is applied across a wire of length L, a uniform electric field is set up inside: E = V / L
3
Each electron experiences a force F = eE. Using Newton's second law and introducing the relaxation time τ (average time between collisions), the drift velocity becomes: vd = eEτ / m = eVτ / (mL)
4
Substituting this expression for vd back into the current equation: I = nAe · (eVτ / mL) = (ne²τA / mL) · V
5
Rearranging gives us: V = (mL / ne²τA) · I. Comparing this with V = IR, we identify: R = mL / (ne²τA). This is exactly V = IR — Ohm's Law, derived from scratch.
🤯

Mind-Blowing Fact

The drift velocity of electrons in a copper wire is shockingly slow — only about 0.1 mm per second. Yet when you flip a light switch, the bulb lights up almost instantly. That's because the electric field — not the electrons themselves — propagates at nearly the speed of light through the wire.


📈 Graphs

V-I Characteristic Graphs

A V-I graph plots Voltage (V) on the y-axis against Current (I) on the x-axis for a specific conductor. The shape of this graph reveals everything about how that conductor behaves electrically.

How to Read the Graph

For an ohmic conductor — such as a metal wire held at constant temperature — the V-I graph is a perfectly straight line passing through the origin. The slope of this line is equal to the resistance of the conductor:

R = V / I = slope of the V-I graph
Steeper slope = higher resistance  |  Flatter slope = lower resistance

A steeper line means more voltage is needed for each unit of current — that material has higher resistance. A flatter line means current flows through it easily — lower resistance. The slope gives you R directly without any calculation errors from individual readings.

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Worked Example

From your V-I graph, when I = 0.4 A the voltage reads V = 2.0 V. Therefore: R = V / I = 2.0 / 0.4 = 5.0 Ω. Pick any other point on that straight line and you'll get the exact same resistance — that's what makes the conductor ohmic.

💡

Why Use the Slope Instead of One Reading?

Drawing the best-fit line and calculating slope averages out all random errors across every data point. A single reading might be off due to measurement mistakes — the slope is far more reliable and is what examiners expect you to use.


⚖️ Comparison

Ohmic vs Non-Ohmic Conductors

Not every conductor obeys Ohm's Law. Understanding this difference is critical for both theory understanding and scoring well in viva and practical exams.

Property Ohmic Conductor Non-Ohmic Conductor
Obeys V = IR? Yes — always (at constant temp) No — R is not constant
V-I Graph Shape Straight line through origin Curved or non-linear
Resistance Value Constant at fixed temperature Changes with voltage or current
Common Examples Copper wire, nichrome, carbon resistors Filament bulb, diode, thermistor, LDR
Why non-ohmic? Temperature changes, junction effects, semiconductor physics
💡

Why Is a Filament Bulb Non-Ohmic?

As more current flows through the filament, it heats up rapidly. In metals, higher temperature causes more lattice vibrations — which means more collisions with electrons — so resistance increases. Since R keeps changing with current, the V-I graph curves upward and the bulb does not obey Ohm's Law.

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The Opposite in Semiconductors

In semiconductors like silicon, increasing temperature actually frees more charge carriers, so resistance decreases with temperature. This is the exact opposite of metals — and it's why thermistors are used as temperature sensors in alarm systems and medical devices.


🧪 Deep Dive

Resistance & Resistivity

Resistance (R) is a property of a specific piece of conductor — it depends on the shape, size, and material. But resistivity (ρ) is an intrinsic property of the material itself. It stays the same no matter how you cut or shape the material. This distinction is fundamental.

R = ρL / A
ρ = resistivity (Ω·m)  |  L = length of wire (m)  |  A = cross-sectional area (m²)

What Affects Resistance?

📏

Length (L)

R increases as length increases. Double the length → double the resistance. R ∝ L

Area (A)

R decreases as area increases. Thicker wire → lower resistance. R ∝ 1/A

🧱

Material (ρ)

Copper: very low ρ → great conductor. Nichrome: high ρ → used in heating elements.

🌡️

Temperature

Metals: R increases with temp. Semiconductors: R decreases with temp.

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Worked Example — Finding Resistance

A nichrome wire has resistivity ρ = 1.1 × 10⁻⁶ Ω·m, length L = 2 m, and diameter d = 0.5 mm.

First, find the area: A = π(d/2)² = π × (0.25 × 10⁻³)² = 1.96 × 10⁻⁷ m²

Then: R = ρL / A = (1.1 × 10⁻⁶ × 2) / (1.96 × 10⁻⁷) = 11.2 Ω

⚠️

Common Mistake — Confusing R and ρ

Students often mix up resistance and resistivity. Remember: resistance R changes if you cut the wire shorter or thicker. Resistivity ρ stays fixed — it is a property of the material, period. A thinner copper wire has higher R than a thick copper wire, but both have the same ρ.


Essential Lab Precautions

🌍 Applications

Where Ohm's Law Rules the Real World

📱

Phone Chargers

Charger circuits use Ohm's Law to regulate voltage and current so your battery charges safely without overheating.

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LED Design

Engineers calculate the exact resistor value using V = IR to protect LEDs from burning out due to excess current.

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Electric Heaters

Heating elements use high-resistance wire — Ohm's Law determines exactly how much heat is produced per second.

🛡️

Fuses & Breakers

Safety fuses are designed knowing exactly what current will flow at dangerous levels — calculated straight from Ohm's Law.

Power Transmission

High-voltage lines carry electricity over long distances with minimal current — reducing I²R heat loss and saving enormous amounts of energy.

🏥

Medical Devices

Pacemakers, ECG machines, and patient monitors all rely on precise resistance calculations to keep patients safe.

🌐

Why Do Power Lines Use High Voltage?

Power transmitted = V × I. To send the same amount of power with much less current, you step the voltage up to hundreds of thousands of volts. Less current flowing through the wire means dramatically less I²R energy lost as heat. This single application of Ohm's Law saves millions of dollars in energy costs every single year.


💬 Viva Prep

Viva Questions & Answers

QUESTION

State Ohm's Law precisely.

ANSWER

At constant temperature, the current flowing through a conductor is directly proportional to the potential difference applied across its ends. Mathematically, V = IR, where R is the resistance of the conductor.

QUESTION

What does the slope of a V-I graph represent?

ANSWER

The slope of the V-I graph — with voltage on the y-axis and current on the x-axis — represents the resistance R of the conductor. A steeper slope indicates higher resistance.

QUESTION

What is the difference between resistance and resistivity?

ANSWER

Resistance (R) depends on the dimensions and material of the conductor, given by R = ρL/A. Resistivity (ρ) is an intrinsic property of the material alone — it does not change when you alter the length or cross-section. Units: R in Ω, ρ in Ω·m.

QUESTION

Why is a filament bulb a non-ohmic device?

ANSWER

As current increases through the filament, its temperature rises significantly. In metals, resistance increases with temperature due to greater lattice vibrations. Since R is not constant, the V-I relationship is not linear — making it non-ohmic.

QUESTION

Why must the ammeter be in series and voltmeter in parallel?

ANSWER

The ammeter has very low internal resistance — in series, it barely affects the current it measures. The voltmeter has very high internal resistance — in parallel, it draws negligible current and gives an accurate voltage reading across the component without disturbing the circuit.

QUESTION

How does temperature affect resistance in metals versus semiconductors?

ANSWER

In metals, rising temperature increases lattice vibrations, causing more electron collisions — so resistance increases. In semiconductors, rising temperature frees more charge carriers — so resistance decreases. This opposite behaviour is why thermistors (semiconductors) are used as temperature sensors.

QUESTION

Why should you calculate R from the graph's slope instead of a single reading?

ANSWER

The best-fit line averages out all random errors from every data point on the graph. A single V and I reading might contain measurement error. Using the slope gives a far more accurate and reliable value of resistance.

QUESTION

What conditions must be satisfied for Ohm's Law to hold?

ANSWER

Ohm's Law holds when: (1) the temperature of the conductor remains constant, (2) the conductor is made of an ohmic material such as a metal, and (3) the physical dimensions and nature of the conductor do not change during the experiment.

🔬 Try the Interactive Ohm's Law Experiment →
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