Resistors — AQA GCSE Physics

An ohmic conductor is one where, at constant temperature, the current is directly proportional to the potential difference. Double the potential difference and the current doubles exactly, so a graph of current against potential difference is a straight line passing through the origin. The line through the origin is the part that proves proportionality; a straight line that misses the origin shows a linear relationship but not a proportional one. A fixed resistor and a length of metal wire behave this way provided they do not warm up. Even a filament lamp is ohmic over a small range near the origin, typically from 0 V to about 2 V, where the current is still too small to heat the filament noticeably.

Direct proportionality has a consequence worth stating separately: if current rises in exact step with potential difference, then V ÷ I is the same at every point, so the resistance stays constant as the current changes. Check it with numbers from a straight line through the origin. At 2 V the current might be 0.4 A, giving 5 Ω; at 6 V it is 1.2 A, giving 5 Ω again. That is what makes a fixed resistor useful, since it behaves predictably whatever the circuit does to it. The reverse test is just as useful: work out V ÷ I at two points on an unfamiliar graph, and if the answers differ the component is not ohmic and something, usually temperature, is changing.

Several common components have a resistance that shifts as conditions change. A filament lamp resists more as the current through it heats the filament. A diode resists almost nothing in the forward direction and hugely in the reverse. A thermistor resists less when its surroundings are hotter, and a light dependent resistor resists less when the light on it is brighter. Their graphs are therefore curved, and you compare two such components at a chosen potential difference. At any given potential difference, the component carrying the smaller current has the larger resistance and its line has the smaller gradient; the one carrying the larger current transfers more energy each second, so a lamp with the larger current is the brighter one.

A filament lamp works by getting hot: current in the thin metal filament raises its temperature until it glows. That heating changes the filament itself. The metal ions in the lattice vibrate more strongly at higher temperature, so the electrons carrying the current collide with them more often and find it harder to pass, which means the resistance increases. The effect shows up clearly on a characteristic graph. Near the origin the line is almost straight, because the current is small and the filament is barely warm. As the potential difference rises the filament heats, the resistance climbs, and the current no longer rises in proportion, so the curve bends over and its gradient falls.

A diode only lets current pass one way. Connected in the forward direction it has a very low resistance once the potential difference is above a small threshold, so the characteristic rises steeply. Reverse the connections and its resistance is very high, so the current stays at effectively zero however far the potential difference is turned up, which is why an ammeter in that circuit reads 0.0 A at every setting. The graph is therefore flat along the reverse side and sharply rising on the forward side. Light emitting diodes behave the same way and emit light only when connected the right way round, which is why they are used as indicators and why diodes are used to protect circuits from reversed batteries.

A thermistor is a resistor whose resistance depends strongly on its temperature: warm it and the resistance falls, cool it and the resistance rises. That makes it a temperature sensor, because a change in surroundings shows up directly as a change in an electrical reading. Put a thermistor in a circuit and the consequences follow from V = I R. As the thermistor warms, its resistance falls, so the total resistance of the circuit falls, so the current from the supply increases and the power transferred increases. The relationship is not a straight line; the resistance falls steeply at first and then more gently, so a thermistor is most sensitive over the temperature range it was chosen for.

Thermistors earn their place in circuits that have to respond to temperature. In a thermostat the thermistor is connected in series with a fixed resistor across the supply, forming a potential divider. As the room warms, the thermistor resistance falls, so the share of the supply potential difference across it falls, and when that reading drops past a set value the control circuit switches the heater off; as the room cools the resistance rises again and the heater comes back on. The same arrangement appears in an oven controller, a fridge, a car engine temperature gauge and a fire alarm, where a sudden rise in temperature produces a sudden fall in resistance that triggers the alarm.

A light dependent resistor, or LDR, responds to light rather than heat: the brighter the light falling on it, the lower its resistance. In darkness its resistance is very high, often hundreds of thousands of ohms, while in bright light it can fall to a few hundred. That makes it a light sensor. In a circuit the consequence again follows from V = I R. Brighter light lowers the resistance of the LDR, which lowers the total resistance of the circuit, so the current from the supply increases. The response is not linear, and the resistance changes over several orders of magnitude, which is why LDR circuits are usually drawn with a fixed resistor beside them to give a workable output.

The obvious use of an LDR is switching lights on when it gets dark. The LDR is placed in series with a fixed resistor across the supply, so as daylight fades the LDR resistance rises, the share of the supply potential difference across it rises, and once it passes a set value the control circuit switches the street lamp or security light on. At dawn the reverse happens and the lamp switches off. The same idea runs a garden light, a night light and the automatic headlights on a car. Other applications use the current directly: a camera adjusts its exposure from the light reaching an LDR, and a burglar alarm triggers when a beam falling on the LDR is broken.

To measure the resistance of a component you need three readings and one equation. Connect the component in series with a cell or battery, an ammeter and a variable resistor, and connect a voltmeter in parallel across the component alone. The ammeter is in series so the current it reads is the current through the component; the voltmeter is in parallel so the potential difference it reads is the one across the component. Adjust the variable resistor, or change the number of cells or the supply setting, to get several pairs of readings, then calculate R = V ÷ I for each and take a mean. Draw the circuit with standard symbols, straight lines and a dot at each junction.

A characteristic graph tells you what a component does. Plot current against potential difference and read the shape. A straight line through the origin means a linear, ohmic element whose resistance is constant, such as a fixed resistor at constant temperature. A curve that bends over with a falling gradient means resistance rising with current, which is a filament lamp heating up. A line that stays at zero one side and rises steeply the other means a diode, which conducts one way only. Anything not a straight line through the origin is non-linear, and for those you calculate R = V ÷ I separately at each point. The shape is never decoration; it is the evidence you quote when explaining what the component is for.

In this required practical you plot characteristics for three components: a resistor at constant temperature, a filament lamp and a diode. Build the same test circuit each time, with the component, an ammeter and a variable resistor in series and a voltmeter across the component, then adjust the variable resistor to take about ten pairs of readings. Reverse the connections to the supply to get negative values, which is essential for the diode, where the reverse readings are all 0.0 A. Plot current against potential difference for each component. A diode needs a protective resistor in series so the forward current cannot damage it, and the resistor must be given time to cool so its temperature stays constant.