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.
This page covers Ohm's law — V = IR — together with current, voltage and resistance, resistors in series and parallel, resistivity, and electrical power. By the end you'll be able to:
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:
Searched as: ohm's law, V = IR, current voltage resistance, resistors in series and parallel, electrical power formula.
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
Type a voltage and a resistance to see what they mean.
In plain terms: voltage is the push, current is the flow, and resistance is what fights it — and V = IR ties all three together.
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.
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.
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
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
| Arrangement | Total resistance | What is shared |
|---|---|---|
| Series | R = R₁ + R₂ + R₃ (adds up) | Same current through each |
| Parallel | 1/R = 1/R₁ + 1/R₂ (drops below smallest) | Same voltage across each |
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.
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.
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.
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.
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.
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.
Voltage pushes, resistance holds back, and current is the steady story they tell together.