Topic B.5 — Current & CircuitsPaper 1 & 2V = IR~6 min read
I–V Characteristics
We’ve been treating resistance like it’s a fixed number for every component — and for some, it really is. But others change their resistance depending on how much current is flowing through them. The best way to spot the difference is to plot current against voltage and look at the shape of the graph.
📘 What You Need to Know
Ohm’s law: for a component at constant temperature, current is proportional to potential difference
V = IR — just Ohm’s law written out, and not one you need to memorise separately from R = V/I
An ohmic component gives a straight-line I-V graph through the origin — a fixed resistor is the classic example
A non-ohmic component’s resistance changes with current, giving a curved I-V graph — filament lamps, diodes, thermistors and LDRs all behave this way
The gradient of an I-V graph tells you the resistance, but which way round depends on which axis current is on
Ohm’s Law: the well-behaved component
Let’s start with the simplest case. If you keep a fixed resistor at a constant temperature and steadily increase the voltage across it, the current increases in exact step with it — double the voltage, and you get double the current. Plot that on a graph of current against voltage, and you get a perfectly straight line through the origin.
Ohm’s lawV = IR
A resistor’s I-V graph is a straight line through the origin — the steady gradient tells you resistance is constant, whatever the voltage.
If current is on the vertical axis and voltage on the horizontal axis (as above), the gradient of that line equals 1/R. Flip the axes around — voltage vertical, current horizontal — and the gradient becomes R itself. Either way, a straight line through the origin means one thing: constant resistance.
The filament lamp: resistance that fights back
Now let’s push more current through a filament lamp. As current rises, the filament heats up — and a hotter filament has a higher resistance, just like we saw in the resistivity lesson. That higher resistance then holds the current back a little. The result is a graph that starts off steep near the origin, then gradually flattens out as voltage increases in either direction.
Near the origin the filament is cool and behaves almost like an ohmic resistor. Further out, it’s hot enough that its rising resistance visibly bends the curve.
The diode: one-way traffic only
A diode is stranger still — it barely lets any current through at all until the voltage is pushing it the “right” way. Connect it so current tries to flow with the arrowhead symbol (forward bias), and past a small threshold voltage, current shoots up steeply. Turn it around (reverse bias), and the diode blocks current almost completely, however hard you push.
A diode’s I-V graph is nowhere near a straight line — it barely conducts at all until the voltage is pushing the right way, then current climbs sharply. LEDs behave the same way.
Quick recap: straight line through origin = ohmic (constant R); curved = non-ohmic (changing R); a filament lamp curves gently as it heats up, a diode barely conducts at all until forward biased.
WE 1
A straight-line I-V graph for a resistor passes through the origin and through the point (6.0 V, 0.40 A). What is the resistance of the resistor?
Since it’s a straight line through the origin, Ohm’s law applies directly:R = V/ISubstitute the point given:R = 6.0 ÷ 0.40R = 15 Ω
WE 2
A student sketches an I-V graph that is steep near the origin and flattens out as voltage increases in either direction, symmetric about the origin. Which component is this most likely to be?
Rule out the resistor:
A fixed resistor gives a straight line, not a curve.
Rule out the diode:
A diode’s graph isn’t symmetric — it barely conducts one way at all.
It’s a filament lamp — its resistance rises as it heats up, flattening the curve at higher voltages
💡 Top Tips
Always check which axis current and voltage are plotted on before reading off resistance from a gradient — it flips the calculation
Look for symmetry: a filament lamp’s curve is symmetric about the origin, a diode’s is not
“Non-ohmic” doesn’t mean “no resistance” — it means the resistance changes rather than staying fixed
⚠ Common Mistakes
Assuming every I-V graph must pass through the origin — diodes clearly show almost zero current for a whole range of reverse voltages
Reading the gradient as resistance without checking which quantity is on which axis
Forgetting that a metal wire only behaves ohmically at a constant temperature — heat it up and its resistance changes too
Up next: Series & Parallel Circuits — now we understand individual components, let’s see how current and voltage behave when several of them share a circuit.
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