Resistance and Ohm's Law

What this lesson covers in the specification

Incandio is aligned to this specification. It is not published by, endorsed by or affiliated with Pearson, and it reproduces none of Pearson's wording — the statement numbers are given so you can check every lesson against your own copy.

• 2.8 — How current in a series circuit depends on applied voltage and the other components
• 2.10 — The qualitative effect of changing resistance on current
• 2.13 — Use V = I × R

Specification section 2(b) Mains electricity — also taught in Series and Parallel Circuits, Current–Voltage Graphs, LDRs and Thermistors, Electrical Power and Energy, Mains Electricity and Safety.

1 · Understand it

No exam language yet. The only question this section answers is: do I actually understand what is happening?

The free electrons drifting through a metal do not have a clear run. The positive ions of the lattice are vibrating on the spot, and the drifting electrons collide with them constantly, losing energy at every collision and being knocked out of their steady drift. RESISTANCE is the measure of how much a component opposes the flow of charge in this way, and the energy the electrons lose ends up as heat in the component — which is why a wire carrying a current gets warm.

The three-way relationship, one variable at a time

1. INCREASE THE VOLTAGE and keep the resistance the same: each coulomb of charge is given more energy, so it is pushed round more forcefully and the current INCREASES. Doubling the voltage doubles the current.
2. INCREASE THE RESISTANCE and keep the voltage the same: the flow of charge is opposed more strongly, so the current DECREASES. Doubling the resistance halves the current.
3. That is statement 2.10 in full: current is proportional to voltage, and inversely proportional to resistance.
4. In a SERIES circuit the components share one path, so adding another component adds its resistance to the total — and the current everywhere in the circuit falls as a result.
5. This is why a series circuit is the awkward one for real installations: every component you add makes every other component dimmer or slower.

Think of it like water pushed through gravel

Picture water forced through a pipe packed with gravel. Raise the pressure at the pump and more water gets through each second. Pack the gravel more tightly and less water gets through for the same pressure. The pressure is the voltage, the flow rate is the current, and the tightness of the gravel is the resistance — and the analogy earns its keep because it explains where the energy goes. The water loses energy pushing past the stones, and it comes out warmer. That is exactly what happens to electrons in a resistor: the energy lost in the collisions appears as heat.

The same picture predicts what length does. A longer pipe of gravel means more stones to push past, so less water gets through for the same pressure. A longer wire means more collisions with ions on the way through, so its resistance is greater — and since every centimetre of the same wire adds the same amount, doubling the length doubles the resistance. You can test exactly this with a metre of wire, two crocodile clips, an ammeter and a voltmeter.

Those relationships are contained in one equation, V = I × R, and it is the most used equation in the whole course. Read it as a definition first: resistance is the voltage needed per ampere of current, R = V ÷ I. A component needing 12 V to drive 2 A has a resistance of 6 ohms. An OHM is simply a volt per ampere.

Using V = I × R three ways

(a) A 6.0 V supply drives 0.40 A through a lamp. What is its resistance? (b) What current flows through a 25 Ω resistor connected to 5.0 V? (c) What voltage is needed to drive 3.0 A through 4.0 Ω?

1. (a) R = V ÷ I = 6.0 ÷ 0.40 = 15 Ω.
2. (b) I = V ÷ R = 5.0 ÷ 25 = 0.20 A.
3. (c) V = I × R = 3.0 × 4.0 = 12 V.
4. In each case identify which quantity is missing, then rearrange before substituting rather than after.

Answer: 15 Ω, 0.20 A and 12 V.

Now the part that is usually skipped, and it is the difference between knowing the equation and understanding it. V = I × R is always true — it is the definition of resistance and it applies to anything. OHM'S LAW is a stronger claim: that for certain components the resistance stays CONSTANT as the current changes, so that current is directly proportional to voltage. Those components are called ohmic conductors, and a fixed resistor or a metal wire at constant temperature is one.

Plenty of things are not ohmic. A filament lamp is the standard example: as the current increases the filament gets hotter, the lattice ions vibrate more violently, the electrons collide with them more often, and the resistance rises. So doubling the voltage across a filament lamp does not double the current — it produces rather less. Ohm's law comes with a condition attached, exactly as Hooke's law does, and the condition is that the temperature must stay constant.

2 · Grade 9 Notes

A different job from the section above. You have already understood it; this is the precise set of things to LEARN — definitions to reproduce word for word, processes in order, equations with units, and the answers that score full marks.

V = I × R

V is voltage in volts (V), I is current in amperes (A), R is resistance in ohms (Ω)

Units: V, A, Ω. Rearranged: I = V ÷ R and R = V ÷ I. An ohm is one volt per ampere.

Learn this definition · Resistance

A measure of how strongly a component opposes the flow of charge through it, equal to the voltage across it divided by the current through it. It is measured in ohms (Ω).

Learn this definition · Ohm's law

The current through an ohmic conductor is directly proportional to the voltage across it, provided the temperature stays constant.

Statement 2.10 — what changing one thing does to the current

• INCREASE THE VOLTAGE, resistance unchanged → current INCREASES, in direct proportion
• INCREASE THE RESISTANCE, voltage unchanged → current DECREASES; double the resistance and the current halves
• ADD A COMPONENT IN SERIES → total resistance increases, so the current everywhere in the circuit falls
• Energy lost by the electrons in collisions with the vibrating ions appears as HEAT in the component

V = I × R against Ohm's law — not the same statement

A. V = I × R is the DEFINITION of resistance and is always true, for any component, at any moment.

B. OHM'S LAW is the further claim that R stays CONSTANT as the current changes, so V is proportional to I. It holds only for ohmic conductors at constant temperature.

Model answer [3 marks]

A 12 V supply is connected across a 48 Ω resistor. Calculate the current. [3]

Rearranging V = I × R gives I = V ÷ R. Substituting, I = 12 ÷ 48 = 0.25 A.

Model answer [4 marks]

Explain why the current through a filament lamp is not proportional to the voltage across it. [4]

As the voltage across the lamp is increased, the current through the filament increases and more energy is transferred to it, so its temperature rises. The positive ions in the metal lattice then vibrate more violently, so the drifting electrons collide with them more frequently and lose energy more often. This means the resistance of the filament increases as it gets hotter. Since the resistance is not constant, the current does not increase in proportion to the voltage, and the lamp is not an ohmic conductor.

Practical — how the resistance of a wire depends on its length

1. Tape a length of thin resistance wire (for example constantan) along a metre rule.
2. Connect the wire in series with an ammeter and a low-voltage supply, using a crocodile clip fixed at 0 cm and a second clip that can slide along the wire.
3. Connect a voltmeter in parallel across the length of wire between the two clips.
4. Set the sliding clip at 10 cm, switch on briefly, record the current and the potential difference, then switch off.
5. Repeat at 10 cm intervals up to 100 cm, then repeat the whole set and calculate a mean resistance R = V ÷ I for each length.
6. Plot resistance against length: a straight line through the origin shows resistance is directly proportional to length.
7. The same circuit can test combinations: two resistors in series give a larger total resistance; two in parallel give less than either one alone.

Variables

Independent (changed) — The length of wire between the clips
Dependent (measured) — The resistance, calculated from V ÷ I

Sources of error

Not this: V = I × R only works for components that obey Ohm's law.

This: V = I × R is the definition of resistance and applies to every component at every instant, including a filament lamp. What fails for a non-ohmic component is that R is not the SAME at every current — so the equation still holds, but with a different value of R each time.

Mark-losing trap. State the condition: Ohm's law holds only if the TEMPERATURE stays constant.

Mark-losing trap. Adding a component in SERIES raises the total resistance, so the current everywhere falls.

Mark-losing trap. Rearrange before substituting. R = V ÷ I, and dividing the wrong way round gives a reciprocal.

3 · Prove it — the five questions

The five questions climb Grade 6 → Grade 7 → Grade 8 → Grade 9 → Grade 9 challenge, and are marked inside Incandio on your own device, by rule, with an authored diagnosis of the mistake you actually made. The mark schemes stay in the app so that the practice is worth doing; the questions themselves are here.

1. Grade 6 · Calculate [2 marks] — A current of 0.50 A flows through a resistor of resistance 24 Ω. Calculate the voltage across it.
2. Grade 7 · State [2 marks] — A second identical resistor is added in series to a circuit, and the supply voltage is unchanged. What happens to the current in the circuit?
3. Grade 8 · Calculate [3 marks] — A 9.0 V battery drives a current of 0.36 A through a component. Calculate the resistance of the component.
4. Grade 9 · Explain [5 marks] — The resistance of a filament lamp increases as the voltage across it is increased. Select every statement that belongs in a full-mark explanation.
5. 9+ · Calculate [5 marks] — A 12 V supply is connected in series with a 40 Ω resistor and a second resistor R. The current in the circuit is 0.20 A. Calculate the resistance of R.

The people behind this science

Two ways into the same idea — the one who thought in fields rather than in equations, and the one who turned those pictures into equations that predict. Inside Incandio each of them answers knowing exactly which lesson you have just finished.

Michael Faraday — the one who thought in fields rather than in equations

Faraday had almost no mathematics and is still one of the greatest experimenters who ever lived, which makes him the right person to ask what resistance IS rather than how to calculate it. He pictured electricity not as a substance travelling in a wire but as a state of strain in the space around it, and insisted on physical pictures where his contemporaries reached for formulae. Anyone who can use V = I × R but could not say what is happening inside the metal is in exactly the position Faraday spent his life arguing against.

• “What do you think is actually happening inside a wire carrying a current?”
• “How did you investigate electricity without using mathematics?”
• “Why did you insist on picturing lines of force in the space around things?”
• “What makes some substances carry electricity and others refuse to?”
• “Where does the energy go when a wire carrying a current becomes warm?”

James Clerk Maxwell — the one who turned those pictures into equations that predict

Maxwell read Faraday's Experimental Researches and did something nobody else had thought worth doing: he took the physical pictures seriously enough to write them as equations. He said explicitly that he wanted to translate Faraday's ideas into mathematical form without adding anything to them — and the result predicted electromagnetic waves travelling at the speed of light. This page is the small-scale version of the same move: a picture of electrons colliding with vibrating ions, turned into V = I × R so that it can predict a number.

• “Why did you set out to put Faraday's ideas into mathematical form?”
• “What can an equation tell you that a physical picture cannot?”
• “How does a relationship between measurements become a law?”
• “What convinced you that light and electricity were the same subject?”
• “Is a law with a condition attached still a law?”

Carry on through the course

• Previous lesson: Charge and Current
• Next lesson: Series and Parallel Circuits
• Charge and Current — What is actually moving in a wire, how fast it is really going, and why the arrows on every circuit diagram point the wrong way.
• Series and Parallel Circuits — Two ways of joining components, and why every building in the world is wired one of them.
• Current–Voltage Graphs, LDRs and Thermistors — The shapes four components make on a graph, and two resistors that deliberately refuse to stay the same.
• Voltage as Energy per Charge — What a volt actually is — and why knowing that turns three separate equations into one idea.
• Electrical Power and Energy — Why a wire carrying a current gets hot, how fast a device uses energy, and how to pick a fuse.
• All of Physics · Physics key terms · required practicals · equations · Incandio Science · The 4PH1 specification