IB Physics HLCurrent & CircuitsPaper 1 & 2Ohm’s Law & Graphs~10 min read
I–V Characteristics
Every component reacts to voltage in its own way. Push more voltage through a plain resistor and the current climbs steadily. Do the same to a lamp or a diode and something stranger happens. The best way to spot the difference is to plot current against voltage — an I–V characteristic. Once you can read the shape of these graphs, you can tell exactly how a component behaves.
📘 What you need to know
Ohm’s law: at constant temperature, current is proportional to voltage, V = IR
An I–V characteristic is a graph of current against potential difference for a component
An ohmic component gives a straight line through the origin (obeys Ohm’s law)
A non-ohmic component gives a curve (does not obey Ohm’s law)
A fixed resistor is ohmic; a filament lamp and diode are non-ohmic
Resistance at any point is R = V / I — and the graph’s shape tells you how R changes
Ohm’s law
Ohm’s law is the rule that ties voltage and current together:
Ohm’s law — in words
For a component at constant temperature, the current through it is proportional to the potential difference across it
The two key words are proportional and constant temperature. If a component keeps its temperature steady, then doubling the voltage doubles the current, tripling it triples the current, and so on. As an equation:
Ohm’s lawV = IR
where V is in volts, I in amperes and R in ohms. A component that obeys this rule is called ohmic. One that doesn’t is non-ohmic. And the quickest way to tell which is which? Plot its I–V graph.
WE 1
A fixed resistor obeys Ohm’s law. When the potential difference across it is 4.0 V, a current of 0.20 A flows. Calculate its resistance.
Step 1 — rearrange Ohm’s lawV = IR, so R = V / IStep 2 — substituteR = 4.0 ÷ 0.20R = 20 ΩBecause it’s ohmic, you’d get the same 20 Ω at any point on its straight-line graph.
Reading an I–V characteristic
An I–V characteristic is simply a graph with current on one axis and potential difference on the other. You build it by slowly changing the voltage across a component and recording the current at each step. The shape that appears is a fingerprint of how the component behaves.
Here’s the golden rule for reading them, straight from R = V/I:
The one rule for reading I–V graphsA straight line through the origin = constant resistance = ohmicA curve = changing resistance = non-ohmic
Here’s the trick that saves you every time: with current on the up-axis and voltage on the across-axis, the steeper the graph, the lower the resistance. Steep line = big current for little voltage = easy flow = low R. A shallow line means the opposite. So watch how the steepness changes as you move along a curve — that’s the resistance changing before your eyes.
The resistor — ohmic
Start with a plain fixed resistor at constant temperature. Increase the voltage and the current rises in perfect step with it. The graph is a straight line straight through the origin — the signature of an ohmic component.
A resistor’s I–V graph is a straight line through the origin. Constant gradient means constant resistance — it’s ohmic.
Because the line is straight, the resistance is the same everywhere on it. You can find it from any point using R = V/I, or from the gradient. A quick note on the gradient:
Gradient of an I–V graphIf I is up, V is across: gradient = I/V = 1 / Rso R = 1 / gradient
WE 2
The I–V graph of an ohmic resistor is a straight line through the origin. It passes through the point (6.0 V, 0.30 A). Use the gradient to find the resistance.
Step 1 — gradient = I / V (line through origin)gradient = 0.30 ÷ 6.0 = 0.05 A V⁻¹Step 2 — resistance is 1 / gradientR = 1 ÷ 0.05R = 20 ΩWhen current is on the y-axis, R is 1 ÷ gradient — not the gradient itself. Easy mark to lose.
The filament lamp — non-ohmic
Now a filament lamp. At low voltages it behaves almost like a resistor — the middle of the graph is nearly straight through the origin. But as you turn the voltage up, more current flows and the thin filament heats up. And remember from the resistance page: a hotter wire has a higher resistance.
So as the lamp brightens, its resistance climbs. The current can’t keep rising as fast, and the line curves over and flattens. That S-shaped curve is the classic non-ohmic signature.
A filament lamp curves and flattens: as it gets hotter, its resistance rises, so the current struggles to keep up.
WE 3
On a filament lamp’s I–V graph, one point reads (2.0 V, 0.50 A) and another reads (8.0 V, 1.0 A). Show that the lamp’s resistance increases, and explain why.
Step 1 — find R at the low-voltage pointR = 2.0 ÷ 0.50 = 4.0 ΩStep 2 — find R at the high-voltage pointR = 8.0 ÷ 1.0 = 8.0 ΩStep 3 — compare and explain
resistance rose from 4.0 Ω to 8.0 Ω
R doubles as the filament heats upHigher voltage → more current → hotter filament → more collisions → higher resistance. Non-ohmic in a nutshell.
The diode — a one-way valve
A diode (and its cousin the LED) is the oddest of the three. It only lets current flow one way:
Forward-biased (connected the “right” way, matching the arrow symbol): almost no current flows until the voltage passes a small threshold, then the current shoots up sharply.
Reverse-biased (connected backwards): the diode blocks the current almost completely — the current stays essentially zero.
A diode blocks current one way (flat at zero) and lets it surge the other way once past a small threshold voltage.
Think of a diode as a one-way turnstile. Push in the allowed direction and, once you shove hard enough (the threshold voltage), everyone floods through. Try to go the wrong way and it simply won’t budge — no current at all. That one-way behaviour is why diodes are used to control the direction of current in circuits.
Putting the three together
Here’s the whole cast summed up. Learn to sketch and recognise these three shapes — examiners love asking you to identify a component from its graph, or to draw one from memory.
Component
I–V shape
Ohmic?
Fixed resistor
Straight line through origin
Yes
Filament lamp
S-curve, flattens out
No
Diode
Flat, then sharp rise one way
No
Straight line through origin
constant R → ohmic
Curve any bend
changing R → non-ohmic
💡 Top tips
Straight line through the origin = ohmic. Any curve = non-ohmic. That one test answers most questions.
Steeper = lower resistance (when I is on the y-axis). Watch the steepness change along a curve.
R = V / I at a point always works — even on a curve. Just read off a coordinate.
Gradient trick: with I up and V across, R = 1 / gradient, not the gradient itself.
Know the three shapes cold: resistor (line), lamp (S-curve), diode (one-way). You may be asked to draw them.
⚠ Common mistakes
Saying the gradient of an I–V graph is the resistance — it’s 1 / gradient when I is on the y-axis
Calling a filament lamp ohmic — it’s non-ohmic; its resistance rises as it heats
Forgetting the “constant temperature” condition in Ohm’s law
Drawing the diode curve rising in both directions — it conducts one way only
Reading resistance off a curve using the gradient instead of R = V/I at that point
Quick recap: An I–V characteristic plots current against voltage. Ohm’s law (V = IR, constant temperature) gives a straight line through the origin for an ohmic component like a fixed resistor. A filament lamp curves and flattens as it heats (resistance rises); a diode conducts one way only. Read resistance at any point with R = V/I.
You can now read how a single component behaves. The next step is wiring several together — and that changes everything about how current and voltage share out. In Series & Parallel Circuits we’ll learn the rules for combining resistors, and see why bulbs in series dim while bulbs in parallel stay bright.
Want to nail these graphs before the exam?
Book a free meeting and we’ll practise sketching and reading every I–V curve together.
