Resistors and Circuit Components

An ohmic conductor is a component whose resistance stays constant as long as its temperature does not change. A fixed resistor at constant temperature is the standard example.

Because the resistance is fixed, rearranging $V=IR$ shows that current is directly proportional to potential difference:

$I=\frac{V}{R}\text{(R constant)}$

Double the potential difference and the current doubles. On a graph of current ($y$-axis) against potential difference ($x$-axis), this gives a straight line through the origin.

The equation $V=IR$ is used throughout this topic. You must recall and apply it; it is not on the Physics equation sheet.

The gradient of a straight I–V line tells you about the resistance: a steeper line means a smaller resistance (more current per volt), a shallower line means a larger resistance.

An I–V characteristic is a graph of current against potential difference for a component. Its shape reveals how the component's resistance behaves. There are three shapes you should be able to recognise and interpret.

Component	Shape of I–V graph	What it tells you
Fixed resistor (ohmic)	Straight line through the origin	Resistance is constant
Filament lamp	S-shaped curve through the origin	Resistance increases as it heats up
Diode	Flat (zero current) for reverse pd, then rising for forward pd	Conducts one way only

The key skill is judging linear versus non-linear: a straight line means constant resistance (ohmic); any curve means the resistance is changing, so the component is non-ohmic.

For a curved graph, resistance at any point is found from the values there using $R=V/I$, not from the gradient (the gradient only gives resistance directly for a straight line through the origin).

A filament lamp contains a thin coil of metal wire, the filament, that glows white-hot when current flows.

As the current increases, the filament gets hotter. In a metal, a higher temperature makes the atoms vibrate more, which obstructs the flowing electrons, so the resistance increases.

This is why the filament lamp is non-ohmic. Its I–V graph is an S-shaped curve through the origin: near the middle the line is steep (low resistance while cool), but as the potential difference and current grow the line bends over, because the rising resistance means each extra volt adds less current.

A filament lamp's resistance increases as its temperature increases. This makes the graph curve; it is not a straight line.

The curve is symmetrical about the origin: reversing the potential difference reverses the current in the same way, because the filament heats up regardless of current direction.

Three more components have a resistance that is not constant.

Diode. A diode lets current flow in one direction only. It has a very high resistance in the reverse direction, so almost no current flows that way. Its I–V graph is flat (zero current) for reverse potential difference, then rises steeply once the forward potential difference is large enough. Diodes are used to protect circuits and to convert alternating current to direct current.

Thermistor. A thermistor's resistance decreases as temperature increases. When it warms up, more current can flow. This makes it ideal for temperature sensing, for example in a thermostat that switches heating on when a room gets cold.

LDR (light-dependent resistor). An LDR's resistance decreases as light intensity increases. In bright light it has low resistance; in the dark its resistance is high. This is used in circuits that switch lights on automatically in the dark, such as street lighting.

Component	Resistance changes with…	Effect	Typical use
Thermistor	Temperature	Resistance falls as temperature rises	Thermostat
LDR	Light intensity	Resistance falls as light rises	Automatic outdoor lighting
Diode	Direction of pd	Very high resistance in reverse	Rectifying / protecting circuits

Aim: obtain the I–V characteristics of a fixed resistor, a filament lamp and a diode at constant temperature.

Apparatus: the test component, a cell or power supply, an ammeter (in series), a voltmeter (in parallel across the component), a variable resistor and connecting leads. The circuit below shows the arrangement for the resistor.

The voltmeter is then connected in parallel across the test component.

Method:

1. Build the circuit with the ammeter in series and the voltmeter in parallel across the component under test.
2. Adjust the variable resistor to change the current, and record the current $I$ and the potential difference $V$ at each setting.
3. Take several readings across a range of potential differences.
4. Reverse the connections to the cell and repeat, so you get negative values of $V$ and $I$ too.
5. Plot $I$ (y-axis) against $V$ (x-axis) and repeat the whole method for each component.

Variable	Type	Detail
Potential difference (set by variable resistor)	Independent	Changed at each reading
Current	Dependent	Measured with the ammeter
Temperature of the component	Control	Keep readings brief so it stays constant

Why use a variable resistor: it lets you change the current without changing the component being tested, so you can plot many points on the same characteristic.

Expected results: the resistor gives a straight line through the origin; the filament lamp gives an S-shaped curve; the diode gives current only in the forward direction.

1. Calling a filament lamp ohmic

A filament lamp is non-ohmic: its resistance rises as it heats, so its graph curves. Only a fixed resistor at constant temperature gives the straight line.

2. Mixing up thermistors and LDRs

A thermistor responds to temperature; an LDR responds to light. Both have resistance that falls as the input (heat or light) rises, but they sense different things.

3. Getting the diode graph the wrong way round

A diode conducts only when the potential difference is in the forward direction. In reverse its resistance is very high, so the current is essentially zero.

4. Reading resistance from the gradient of a curve

For a curve, work out resistance at a point using $R=V/I$ with the values at that point. The gradient only gives resistance directly for a straight line through the origin.

5. Forgetting to keep the temperature constant

If the component heats up during the test (especially the resistor), its resistance drifts and the line stops being straight. Take readings quickly and keep the current modest.