IB Physics HLCurrent & CircuitsPaper 1 & 2R = V / I~9 min read
Electric Resistance
Even the best conductors don’t let charge through for free. As electrons drift along a wire, they keep bumping into things — and every bump slows them down and gives off heat. That opposition to the flow is resistance. On this page we’ll see why it happens deep inside the metal, meet the equation R = V/I, and learn what makes an ammeter or voltmeter “ideal”.
📘 What you need to know
Resistance is a measure of how much a component opposes the flow of current
It’s caused by electrons colliding with the metal ions, transferring energy that heats the wire
Resistance R = potential difference ÷ current, i.e. R = V / I
It’s measured in ohms (Ω) — the Greek letter omega
The higher the resistance, the smaller the current for a given voltage
An ideal ammeter has zero resistance; an ideal voltmeter has infinite resistance
Why does a wire resist?
Picture the electrons drifting through the metal lattice. It’s not a clear run — the wire is packed with positive metal ions sitting in the way. As the electrons move, they keep colliding with these ions.
Every collision hands a little of the electron’s energy to an ion. The ions start vibrating harder — which, at the large scale, means the wire heats up. So the electrons are constantly being knocked about and slowed down. That opposition to their flow is what we call resistance.
The electron can’t travel in a straight line — it bounces off ion after ion, losing energy as heat each time. That’s resistance in action.
Here’s the picture that makes it stick: imagine running through a crowded room. In an empty room you’d sprint straight across. In a packed one you keep bumping into people, zig-zagging, slowing down — and you’d get warm doing it. Electrons in a wire feel the same thing. The “crowd” is the metal ions, and resistance is how hard it is to get through.
Some metals have more crowded, obstructive lattices than others, so they resist more. Copper has a low resistance, which is exactly why we make wires out of it — charge gets through easily. And a key idea for later: the more a wire heats up, the higher its resistance climbs.
Measuring resistance: R = V / I
We define the resistance of a component as the ratio of the potential difference across it to the current flowing through it:
Resistance — definition
The ratio of the potential difference across a component to the current through it
As an equation, that’s:
Resistance equationR = V / I
Where:
R = resistance, in ohms (Ω)
V = potential difference, in volts (V)
I = current, in amperes (A)
Read it as a story: for the same push (voltage), a component with high resistance only lets a small current through. Turn the resistance down and the current goes up. The two trade off against each other.
Big push (high V)
but lots of opposition (high R)
Small flow (low I)
The unit of resistance is the ohm, written with the Greek letter Ω (omega). In SI base units, 1 Ω = 1 kg m2 s−3 A−2 — but you’ll almost always just use volts over amps.
WE 1
A potential difference of 6.0 V across a resistor drives a current of 0.5 A through it. Calculate its resistance.
Step 1 — write the equationR = V / IStep 2 — substituteR = 6.0 ÷ 0.5R = 12 ΩVolts on top, amps on the bottom — the answer comes out in ohms.
WE 2
A charge of 8.0 C flows through a component in 20 s while a potential difference of 3.0 V is applied. Calculate the resistance of the component.
Step 1 — find the current firstI = Δq / Δt = 8.0 ÷ 20 = 0.4 AStep 2 — now use R = V / IR = 3.0 ÷ 0.4R = 7.5 ΩTwo-step questions are common: get the current from charge and time, then feed it into R = V / I.
WE 3
A current of 250 mA flows through a lamp when 5.0 V is applied across it. Calculate its resistance. (Watch the units!)
Step 1 — convert mA into A250 mA = 250 × 10⁻³ A = 0.25 AStep 2 — use R = V / IR = 5.0 ÷ 0.25R = 20 ΩIf you’d left the current as 250, you’d have got a nonsense answer. Always convert mA → A first.
Resistance and heat — a useful pair
Because resistance produces heat, it’s not always a nuisance. In a kettle or a toaster, a special high-resistance wire is used on purpose, so it gets hot enough to boil water or brown your bread. In a connecting wire, though, we want low resistance so almost no energy is wasted as heat — which is why copper wins.
Ideal meters
Every real component has some resistance — even the wires and the battery. That includes the measuring instruments. To avoid disturbing the circuit they’re reading, we describe meters as ideal:
Ideal ammeter: zero resistance, so it doesn’t slow the current. Ideal voltmeter: infinite resistance, so no current leaks off through it.
An ideal ammeter has zero resistance. It sits in series, so if it had any resistance it would reduce the very current it’s trying to measure. Zero resistance = no interference.
An ideal voltmeter has infinite resistance. It sits in parallel, so infinite resistance means (almost) no current sneaks through it — it reads the p.d. without stealing any charge.
In exams, unless a question says otherwise, treat every ammeter and voltmeter as ideal. That’s a gift — it means you can ignore the meters’ resistance completely when working out the circuit. Only worry about meter resistance if the question specifically gives you a value for it.
💡 Top tips
R = V / I — volts over amps. Rearranges to V = IR and I = V/R.
Convert units first: mA → A and kV → V before dividing, or your ohms will be wrong.
High resistance → small current (for a fixed voltage). Low resistance → big current.
Resistance comes from collisions — electrons hitting ions, giving off heat.
Writing R = I / V — it’s the other way up, V over I
Forgetting to convert mA into A (or kV into V) before using the equation
Saying resistance is caused by electrons hitting each other — it’s electrons hitting the ions
Swapping the ideal resistances (ammeter is zero, voltmeter is infinite)
Thinking a higher voltage always means a higher current — it also depends on the resistance
Quick recap: Resistance is the opposition to current, caused by electrons colliding with metal ions and heating the wire. It’s found from R = V/I and measured in ohms (Ω). Higher resistance means a smaller current for the same voltage. Ideal ammeters have zero resistance; ideal voltmeters have infinite resistance.
We’ve seen that a wire resists — but what actually sets how much? A thin wire resists more than a fat one; a long wire more than a short one; and the material matters too. In the next page, Electrical Resistivity, we’ll turn all of that into a single tidy equation and discover the property that captures how “resistive” a material is by nature.
Want resistance to click before the exam?
Book a free meeting and we’ll work through the collisions, the equation and the meters together.
