🟢 Electricity · Class 9–12 · Boards + AP + Olympiad

Push harder, more flows

Ohm's law · current · voltage · resistance · series & parallel · electrical power

Electricity is just charge on the move. Give it a bigger push — more voltage — and more of it flows. Put something in the way — more resistance — and less gets through. Ohm's law, V = IR, ties those three together into the one relationship behind every circuit you will ever meet.

Voltage · the pushCurrent · the flowResistance · what fights itV = IR · the whole law
What you'll learn

Ohm's Law — the heart of every circuit

This page covers Ohm's lawV = IR — together with current, voltage and resistance, resistors in series and parallel, resistivity, and electrical power. By the end you'll be able to:

  • Use V = IR to find any one of voltage, current or resistance.
  • Read a V–I graph and tell an ohmic conductor from a non-ohmic one.
  • Combine resistors in series (they add) and in parallel (they divide).
  • Find a wire's resistance from its length, thickness and material (R = ρL/A).
  • Calculate electrical power three ways — P = VI, P = I²R and P = V²/R.
Why it matters · where it's tested

The most-wired topic in school physics

Every switch, charger, bulb and heater runs on these rules — and electricity is among the most-tested chapters at every level. We go beyond the syllabus, but we never skip it:

CBSE · Class 10 — Electricity CBSE · Class 12 — Current Electricity ICSE / NCERT IGCSE · Cambridge / Edexcel — Electricity AP Physics — Circuits Olympiad — NSO · NSEJS · IPhO foundations

Searched as: ohm's law, V = IR, current voltage resistance, resistors in series and parallel, electrical power formula.

See it live

Choose what to solve for, type the other two values, and the circuit answers — current flowing through the resistor, with a live V–I graph beside it. 🟢 real Ohm's-law engine

Ohm's law circuit

Voltage6 V
Current2 A
Resistance3 Ω
Power12 W
Solve for
I = V ÷ R = 6 ÷ 3 = 2 A

Type a voltage and a resistance to see what they mean.

What's going on

In plain terms: voltage is the push, current is the flow, and resistance is what fights it — and V = IR ties all three together.

What it is

Current is the flow of electric charge — how much passes a point each second, measured in amperes. To make it flow you need a push, and that push is the voltage (or potential difference), the energy each unit of charge carries, measured in volts. Standing in the way is resistance, how strongly the material opposes the flow, measured in ohms. More push gives more current; more resistance gives less. That is the whole intuition, before a single formula.

How the principle works

Ohm found that for a metal conductor at constant temperature, the current is directly proportional to the voltage — double the push, double the flow. Writing the fixed ratio of voltage to current as the resistance R gives V = IR, the three faces of one law: I = V ÷ R, V = IR, and R = V ÷ I. A conductor that obeys this is ohmic, and its V–I graph is a straight line through the origin. A filament lamp is non-ohmic: it heats up, its resistance climbs, and the line bends into a curve.

How it works in the calculator

The circuit above is an Ohm's-law machine. Tell it which quantity you want — voltage, current or resistance — type the other two, and it applies V = IR to find the third, then shows the power P = VI the resistor turns into heat and light. The animated dots flow faster when the current is larger, the resistor's value sets how hard they are pushed through, and the V–I graph plots your working point on the straight line whose slope is the resistance. 🟡 maths of the picture

Edge cases
  • Double the resistance → half the current, for the same voltage (I = V ÷ R).
  • Zero resistance (a short circuit) → a huge current — which is exactly why shorts are dangerous.
  • Series adds, parallel divides — adding a parallel path lowers the total resistance below the smallest resistor.
  • Non-ohmic parts (lamps, diodes) don't keep a constant R, so V = IR only holds moment to moment.
Three points & measures
  • Voltage (V) — the push, in volts.
  • Current (I) — the flow of charge, in amperes; the calculator's animated dots.
  • Resistance (R) — the opposition, in ohms; with power P = VI in watts.

See the maths

The physics is visible in the diagram; the maths usually hides. These little labs make it visible too — drag a slider and watch the numbers and arrows answer.

📏 Resistance of a Wire

A wire's resistance follows R = ρL ÷ A: longer means more resistance, thicker means less. Slide the length and the thickness and watch R respond (nichrome, ρ ≈ 1.1×10⁻⁶ Ω·m).
Length
1.0 m
Section
0.5 mm²
Resist.
2.2 Ω
R = ρL ÷ A = 2.2 Ω

🔗 Series vs Parallel

Put equal resistors in a row and resistance adds; put them side by side and it divides. Choose how many and which way, and watch the total.
Layout
Series
Total R
6.0 Ω
3 × 2 Ω in series = 6 Ω

📈 V–I Characteristic

An ohmic resistor gives a straight line — constant resistance. A filament lamp curves, because it heats up and its resistance climbs. Flip between them.
A resistor obeys V = IR — a straight line through the origin, constant resistance.

In the real world

The dimmer switch

Slide a dimmer and the room fades or brightens. Inside, you are changing the resistance in series with the bulb — more resistance means less current (I = V ÷ R), and a softer glow. Less resistance lets more current through, and the room lights up.

The fuse

A fuse is a thin wire built to be the weakest link. If too much current flows, the heating P = I²R melts it and breaks the circuit before the rest of the wiring can overheat or catch fire. A small sacrifice that protects the whole house.

The bird on a wire

A bird perches on a bare power line unharmed because both feet sit at almost the same voltage — there is no potential difference across it, so no current flows through it. Touch a second wire at a different voltage, and the story would change.

Build it yourself — science-fair projects

Physics you can hold. Each project below demonstrates a law you just met — and the measuring is what turns a demo into a science-fair winner. Pick one, build it from things at home, and graph something.

🍋Beginner

Fruit battery

Shows · voltage & current from a cell

Build: push a copper coin and a zinc nail into a lemon or potato; chain several in series to light a small LED.

Measure: the voltage of one cell with a multimeter, then how many cells in series it takes to light the LED.

✏️Beginner

Pencil dimmer

Shows · resistance changes current

Build: draw a thick graphite line on paper, wire a battery and a bulb to it, and slide one contact along the line.

Measure: brightness versus how far apart the contacts are — a longer graphite path means more resistance.

🔆Intermediate

Series vs parallel bulbs

Shows · voltage sharing

Build: wire two or three identical bulbs first in series, then in parallel, from the same battery.

Measure: compare the brightness; in series they dim and share the voltage, in parallel each stays bright.

🌊Intermediate

Salt-water conductivity

Shows · resistance & resistivity

Build: dip two electrodes in a cup of water with a bulb in the circuit, then stir in salt a spoon at a time.

Measure: brightness (or current) against salt added — more salt lowers the resistance, so more current flows.

🔌Intermediate

Multimeter resistance hunt

Shows · R = V ÷ I

Build: measure the resistance of everyday things — a pencil lead, your skin, a resistor — with a multimeter.

Measure: rank them from low to high, and check a resistor's reading against its colour-code value.

📏Champion

Wire-length resistance lab

Shows · R = ρL ÷ A

Build: tap a battery and meter at points along a long resistance wire to read the resistance of each length.

Measure: plot resistance against length — a straight line — then try a thinner wire and watch the slope rise.

Glossary — the 10 words that unlock it

Electric current

What it means
The flow of electric charge — how much passes a point each second, in amperes.
Why it matters
It is the actual electricity that lights, heats and drives things.
Example
A small torch bulb might draw about 0.3 A.
Key question
What is actually moving when a current flows in a metal?

Voltage

What it means
The electrical push between two points — the energy given to each unit of charge, in volts.
Why it matters
Without a voltage there is nothing to make the charge flow.
Example
A single dry cell provides about 1.5 V.
Key question
What does raising the voltage do to the current?

Resistance

What it means
How strongly a component opposes the current, equal to V ÷ I, in ohms.
Why it matters
It decides how much current a given voltage can push through.
Example
A small bulb might have only a few ohms of resistance.
Key question
What two things about a wire change its resistance?

Ohm's law

What it means
For an ohmic conductor at constant temperature, V = IR.
Why it matters
It links voltage, current and resistance into one usable equation.
Example
6 V across a 3 Ω resistor gives a 2 A current.
Key question
When does Ohm's law stop holding true?

Resistor

What it means
A component made to provide a set resistance and limit the current.
Why it matters
It protects parts and sets currents to safe, useful values.
Example
The coloured bands on a resistor give its value in ohms.
Key question
Why might a circuit need to limit its current?

Conductor

What it means
A material that lets charge flow easily, because it has many free electrons.
Why it matters
Wires are conductors so current can travel where we want it.
Example
Copper and aluminium are excellent conductors.
Key question
What makes a metal conduct so well?

Resistivity

What it means
A property of the material itself setting how strongly it resists current; R = ρL ÷ A.
Why it matters
It lets you compare materials regardless of a wire's shape.
Example
Nichrome has a high resistivity, so it is used in heaters.
Key question
Why is a heater's wire nichrome, not copper?

Series

What it means
Components joined end to end in a single path.
Why it matters
The same current flows through each, and their resistances add.
Example
Old fairy lights in series all dim when you add more.
Key question
What happens to the others if one series bulb fails?

Parallel

What it means
Components joined across the same two points.
Why it matters
Each gets the full voltage and works independently of the others.
Example
The sockets in a house are wired in parallel.
Key question
Why does the total resistance fall when you add a parallel path?

Electrical power

What it means
The rate a component turns electrical energy into heat, light or motion; P = VI.
Why it matters
It tells you how bright a bulb is or how fast a heater warms up.
Example
A 60 W bulb on 240 V draws about 0.25 A.
Key question
Which two cousins of P = VI bring in the resistance?

The questions people ask

Ohm's law sits under every circuit you use. Here are the questions that come up most — each answer reads on its own, lifted clean off the page.

What is Ohm's law and how is it used?
ConceptualWhatcomplexity 2

Ohm's law states that for an ohmic conductor at constant temperature, the voltage across it is proportional to the current through it, written V = IR, where R is the resistance. To use it, keep any two of the three quantities and find the third: I = V/R for current, V = IR for voltage, and R = V/I for resistance. It is the basic tool for working out currents, voltages and resistances in simple circuits.

What is the difference between current, voltage and resistance?
ComparativeWhatcomplexity 2

Current is the rate at which charge flows, measured in amperes; voltage is the electrical push, or energy per unit charge, measured in volts; and resistance is how strongly a component opposes the current, measured in ohms. In the water analogy, current is the flow rate, voltage is the pressure, and resistance is how narrow the pipe is. Ohm's law ties them together as V = IR.

What is the difference between an ohmic and a non-ohmic conductor?
ComparativeWhatcomplexity 3

An ohmic conductor obeys Ohm's law: its current is directly proportional to the voltage, so its V–I graph is a straight line through the origin and its resistance stays constant. A non-ohmic component, such as a filament lamp or a diode, does not: as the current changes, its resistance changes too (a lamp heats up and its resistance rises), so its V–I graph is a curve rather than a straight line.

How do resistances combine in series and in parallel?
How-ToHowcomplexity 4
ArrangementTotal resistanceWhat is shared
SeriesR = R₁ + R₂ + R₃ (adds up)Same current through each
Parallel1/R = 1/R₁ + 1/R₂ (drops below smallest)Same voltage across each
Why does a wire heat up when current flows through it?
ScenarioWhycomplexity 3

A wire heats up because the flowing electrons collide with the atoms of the material and lose energy to them, which appears as heat. This is resistive (Joule) heating, and the power turned into heat is P = I²R, so it grows quickly with current and with resistance. It is why long thin wires warm up, why fuses melt when overloaded, and how electric heaters and toasters work on purpose.

What is resistivity and what does it depend on?
ConceptualWhatcomplexity 3

Resistivity is a property of the material itself that sets how strongly it resists current, independent of the wire's shape. The resistance of a wire is R = ρL/A, where ρ is the resistivity, L the length and A the cross-sectional area. So a longer or thinner wire has more resistance, a shorter or thicker wire less, and metals like copper have a low resistivity while alloys like nichrome have a high one.

How do you calculate electrical power?
How-ToHowcomplexity 3

Electrical power is the rate at which energy is delivered, P = VI, the voltage times the current, measured in watts. Using Ohm's law you can rewrite it in two handy forms: P = I²R (when you know the current and resistance) and P = V²/R (when you know the voltage and resistance). All three give the same answer; you pick whichever pair of quantities you already know.

Why are household appliances connected in parallel?
ScenarioWhycomplexity 3

Household appliances are wired in parallel so that each one gets the full mains voltage and works at its proper power, and so that each can be switched on or off independently without affecting the others. If they were in series, the voltage would be shared among them, they would all dim, and one appliance failing would break the circuit for all. The cost of parallel wiring is a larger total current, which is why homes need fuses and thick cables.

What is a short circuit and why is it dangerous?
ReflectiveWhycomplexity 4

A short circuit is an accidental low-resistance path that lets current bypass the intended components. Because the resistance is very small, Ohm's law (I = V/R) gives a very large current, which heats the wires through P = I²R and can melt insulation or start a fire. Fuses and circuit breakers protect against this by cutting off the supply when the current rises above a safe limit.

Test yourself — a mixed set

Seven question formats, the way Beyond Dictionary serves them — multiple choice, multiple-correct, fill-in-the-blank, match, sequence, read-think-connect, and write-your-own. Every question has layered hints: a quick nudge, the reasoning, then a deeper connection — so a wrong answer opens a door, never a dead end. 🟢 received from a board-tagged question bank · seed toward 2,000

Pick your board — the set re-tunes to its wording and emphasis. Competitive draws the JEE / NEET / Olympiad lane.

Loading the question bank…
Question 1 of 16
Multiple choice

Key takeaways

  • V = IR ties voltage, current and resistance into one law.
  • More voltage means more current; more resistance means less — for the same supply.
  • Series resistances add; parallel resistances divide — a parallel total drops below the smallest resistor.
  • Electrical power is P = VI — and, using Ohm's law, also I²R and V²/R.
  • Ohmic gives a straight V–I line (constant resistance); a heating filament curves (non-ohmic).

🪜 Where this lesson leads

Ohm's law is the doorway into electric circuits. Master it and you have already started climbing toward:
Current & voltage
Resistance
Series & parallel
Electrical power
Kirchhoff's laws
Capacitors
Electromagnetism
Electronics

Keep exploring

Voltage pushes, resistance holds back, and current is the steady story they tell together.

Copyright © Pawan Nayar · LLOS.ai · 2026 — Original pedagogy, voice, and design — all rights reserved.
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