I–V Characteristics

Every electrical component has a personality. Push a potential difference across it and a current flows — but how much current, for how much push, is different for a plain resistor, a light bulb, or a diode. The neatest way to capture that personality on paper is a single graph: plot the current I through the component (up the vertical axis) against the potential difference V across it (along the horizontal axis).

That graph is the component's I–V characteristic. Its shape is a fingerprint: a straight line, a lazy S, or a one-sided ramp — and from that shape you can read straight off how the component's resistance behaves. This one idea — shape of the curve tells you the resistance — is what the whole page is about.

How you actually get the graph

You don't just read a characteristic out of a book — you measure it. Build a simple test circuit around the component you want to investigate:

an ammeter in series with the component, to read the current I through it;
a voltmeter in parallel across the component, to read the potential difference V across it;
a variable resistor (a rheostat) in the circuit, which you slide to change the pd across the component a little at a time.

Now the routine: set the variable resistor, write down the pair of readings (V, I), nudge the resistor, take another pair — and so on. To get the whole characteristic you also reverse the supply so you sweep negative pd as well as positive, which is how the left-hand half of every graph below gets drawn. Plot all your points, join them up, and the characteristic appears.

You could change the pd by turning the power supply's dial — but a variable resistor gives you far finer, steadier control, and it protects the component: you can ease the current up gently instead of slamming a big voltage across a delicate filament or diode. It also lets you take lots of closely spaced readings near the interesting bends in the curve, where the shape matters most. Good data means many points, not four.

The ohmic resistor: a straight line through the origin

Start with an ordinary fixed resistor kept at a constant temperature. Take your readings and its characteristic is the simplest possible: a straight line passing through the origin. Double the pd and the current doubles; treble it and the current trebles. Current and pd rise in exact proportion, I \propto V.

A straight line through the origin means one thing: the resistance never changes. Pick any point on the line and work out R = V/I and you get the same answer every time. A component that behaves like this is called ohmic, because it obeys Ohm's law.

For an ohmic conductor kept at constant temperature, the current is directly proportional to the potential difference across it:

V = I\,R,\qquad R = \frac{V}{I}.

The resistance R is constant, so the I–V graph is a straight line through the origin.
The line's gradient is \dfrac{I}{V} = \dfrac{1}{R} — a steeper line means a smaller resistance (more current for the same pd).

Watch that last point carefully: the gradient is 1/R, not R. A low-resistance resistor lets a big current through for a small pd, so its line is steep; a high-resistance one is shallow. Same straight-line shape, different steepness.

The filament lamp: an S-shaped curve that flattens

Now test a filament lamp — the thin wire inside an old-style bulb. Its characteristic is not a straight line. It comes out as a stretched S-shape: steep near the origin, then curving over and flattening as the pd grows (and mirror-imaged on the negative side).

Why? Because pushing current through the thin filament makes it hot — hot enough to glow. And a hot metal wire has a higher resistance than a cold one: its atoms jiggle more and get in the way of the flowing charge. So as you increase the pd, the lamp heats up, its resistance rises, and each extra volt buys you less extra current than the last. The line bends over. A filament lamp is non-ohmic: it breaks Ohm's law precisely because it won't stay at constant temperature.

You can prove the resistance is rising straight from the graph. Read off R = V/I at a point low down — say V = 2\,\text{V}, I = 1.5\,\text{A}, giving R \approx 1.3\,\Omega. Now read a point high up — say V = 6\,\text{V}, I = 3\,\text{A}, giving R = 2\,\Omega. Same lamp, bigger resistance when hotter.

The diode: a one-way valve

Last, test a diode. Its characteristic is the most lopsided of all. Sweep the pd backwards (reverse) and almost no current flows at all — the line hugs the horizontal axis. Sweep it forwards and, once the pd creeps past a small threshold (about 0.6\,\text{V} for a silicon diode), the current suddenly shoots up, almost vertically.

In plain words: a diode lets current flow one way only. Forwards it eventually conducts freely; backwards it blocks. Its resistance is enormous in reverse and tiny once it's switched on forwards — anything but constant, so a diode is very much non-ohmic too. This one-way behaviour is exactly why diodes are used to steer current where it's wanted and keep it out of where it isn't.

See all three side by side

Below is a live I–V graph. Use the first control to switch between the resistor, the filament lamp and the diode, and watch the characteristic redraw. Then slide the second control to move a reading-off point along the curve: the dashed lines drop to the axes and the box works out R = V/I right there. Notice how, for the resistor, that R stays the same wherever you put the point — while for the lamp it climbs as you move to higher pd.

A curved line means the resistance is CHANGING. A straight line through the origin is the only shape that means constant resistance. The filament lamp's curve isn't "a resistor with a wobble" — it bends because its resistance genuinely rises as it heats. Curve ⇒ non-ohmic.
To find R at a point, use R = V/I at that point — never the gradient of a curve. The gradient trick (\text{gradient} = 1/R) only works for the straight ohmic line. On a curve, you must read the actual V and I of the point and divide.
The diode conducts one way only. The near-flat reverse part isn't a mistake in your readings — the diode really is blocking the current. Don't expect it to be symmetric like the resistor and lamp.
Gradient is 1/R, not R. A steeper ohmic line is a smaller resistance, because it delivers more current per volt.

When you dim an old filament bulb you're sliding it up and down its own I–V curve. Turn the pd down and you move towards the origin, where the line is steep — the cool filament has a low resistance. Turn it up and you climb into the flat part, where the glowing-hot filament fights back with a much higher resistance. That temperature-driven rise in resistance is also why a cold bulb draws a big inrush of current the instant you switch it on, and why filament bulbs so often blow at that first flick rather than while they're steadily lit — the surge happens before the filament has heated up and pushed its resistance back up.