Variable resistors

What does a variable resistor do?

A variable resistor lets you adjust a circuit by hand. In series with a lamp, more resistance means less current, so the lamp gets dimmer. Less resistance means more current and a brighter lamp. It follows from the relationship between current, potential difference (voltage) and resistance:

With the supply voltage fixed, raising R lowers I. A variable resistor is simply a way of choosing R while the circuit is running.

How a variable resistor works

Inside is a track of resistive material, such as carbon or a coil of thin wire, and a sliding contact called the wiper that presses on it. Current flows through the part of the track between one end and the wiper. The resistance of a uniform track is proportional to its length, so moving the wiper changes how much track the current passes through, and so the resistance.

This is the same idea as the GCSE resistance practical, where you measure the resistance of different lengths of wire and find that doubling the length doubles the resistance. A variable resistor builds that experiment into one component.

Variable resistor symbol

In UK circuit diagrams, a fixed resistor is a rectangle. A variable resistor is the same rectangle with a diagonal arrow drawn through it, showing the resistance can be changed. A potentiometer is drawn as a rectangle with an arrow pointing at its side, which stands for the wiper touching the track. US diagrams draw resistors as zigzag lines, with the same arrows.

Fixed resistor:      ──[      ]──

Variable resistor:   ──[  ／  ]──     (an arrow drawn diagonally through the box)

Potentiometer:       ──[      ]──
                          ↑
                        wiper

Potentiometer vs rheostat

The same physical part can do either job. A potentiometer has three pins: use the wiper and one end, and it behaves as a rheostat. Lab rheostats are often big wire-wound tubes with a sliding contact on top, because they must carry larger currents and get warm.

Types of variable resistor

• Rotary: a knob turns the wiper round a curved track, as on a volume control.
• Slider: the wiper moves along a straight track, as on the faders of a sound mixing desk.
• Trimmer (preset): a tiny one on a circuit board, set once with a screwdriver.

Potentiometers also differ in how the resistance changes as you turn them. A linear one changes evenly: halfway round gives half the resistance. A logarithmic (audio) one changes slowly at first and then quickly. Our ears judge loudness on a roughly logarithmic scale, so an audio taper makes a volume knob feel even across its whole turn.

Using a rheostat to control current

Example: a 12 V supply, a lamp with a resistance of 6 Ω and a 0 to 18 Ω rheostat are connected in series. Treat the lamp's resistance as constant. What range of current can the rheostat give?

• Rheostat at 0 Ω: total resistance 6 Ω, so I = 12 ÷ 6 = 2 A, the brightest setting.
• Rheostat at 18 Ω: total resistance 6 + 18 = 24 Ω, so I = 12 ÷ 24 = 0.5 A, the dimmest setting.

In series, resistances add (see resistors in series and parallel), so the rheostat can only ever reduce the current. It can't reach zero, and it wastes energy: at 0.5 A the rheostat turns 0.5² × 18 = 4.5 W into heat while the lamp only gets 0.5² × 6 = 1.5 W. That is why modern mains dimmer switches use electronic circuits that switch the power on and off rapidly instead.

Using a potentiometer as a potential divider

A potential divider splits the supply voltage between two resistances in series. A potentiometer is a potential divider in one part: the wiper splits the track into a top part and a bottom part, and the output voltage is taken across the bottom part. Move the wiper up and the output rises, from 0 V at the bottom to the full supply at the top.

Example 1: a 10 kΩ potentiometer is connected across a 9 V battery, with the wiper 30% of the way up the track. The bottom part is 3 kΩ and the top part 7 kΩ, so the output is 9 × 3 ÷ 10 = 2.7 V. Because the track is uniform, the output is simply 30% of 9 V.

Example 2: a fixed 2 kΩ resistor R₁ is in series with a 0 to 10 kΩ variable resistor R₂ across 9 V, and the output is taken across R₂. With R₂ set to 4 kΩ, the output is 9 × 4 ÷ (2 + 4) = 6.0 V. Turned to its maximum, 10 kΩ, the output is 9 × 10 ÷ 12 = 7.5 V. The fixed resistor stops the output ever reaching the full 9 V.

Potential dividers are an A-level topic. AQA's A-level Physics specification says examples should include variable resistors, thermistors and light dependent resistors (LDRs) in a potential divider. Try a calculation yourself, then press Mark to check it in our Circuits course.

Variable resistors in the I-V characteristics practical

In AQA GCSE Physics, required practical 4 asks you to investigate the I-V characteristics of a filament lamp, a diode and a resistor at constant temperature. The variable resistor is what lets you take a set of readings.

1. Build a single loop of the supply, the variable resistor, the ammeter and the component. Then connect the voltmeter across the component on its own.
2. Set the variable resistor to its highest resistance, then record the current and the potential difference.
3. Lower the resistance in steps, recording both readings each time. Each step gives a bigger current and a bigger potential difference across the component.
4. Reverse the connections to the component to get negative values, and repeat.
5. Plot current against potential difference.

A resistor at constant temperature gives a straight line through the origin. A filament lamp's line curves as it heats up, because its resistance rises. A diode conducts in one direction only, so the current stays near zero when it is reversed. Some schools use a variable power supply instead of a variable resistor, which does the same job of changing the potential difference.

Where variable resistors are used

• Volume and tone controls: electric guitars and many amplifiers use potentiometers on their knobs.
• Joysticks and game controllers: analogue sticks often contain two potentiometers, one for each direction, so the voltage tells the console the stick's position.
• Motor speed: model railway controllers and some fans.
• Fuel gauges: in many cars, a float in the tank moves the wiper of a variable resistor as the fuel level changes.
• Sensor circuits: a variable resistor in a potential divider with a thermistor or LDR sets the temperature or light level at which something switches on.
• Trimmers: small preset variable resistors on circuit boards, adjusted once with a screwdriver to fine-tune a circuit.

Variable resistors vs thermistors and LDRs

A thermistor's resistance changes with temperature, and an LDR's with light. Their resistance varies, but not because you turn a knob, so they count as sensors rather than variable resistors. They often work together: in a potential divider, a variable resistor sets the point at which the sensor's change triggers an output.

Worked example: resistance from the slider position

A rheostat has a uniform track 50 cm long with a total resistance of 20 Ω. The slider is 15 cm from the end in use. What resistance is in the circuit? Each centimetre is 20 ÷ 50 = 0.4 Ω, so 15 cm gives 15 × 0.4 = 6 Ω. You can build circuits like these and watch the current change in the Circuit Builder.

Common mistakes

• Drawing the wrong symbol. The variable resistor has the arrow through the box. A thermistor and an LDR have their own symbols.
• Thinking a rheostat can cut the current to zero. It can only add resistance up to its maximum, so the current falls to a minimum, not zero.
• Putting the voltmeter in series in the I-V practical. The ammeter goes in series and the voltmeter across the component.
• Using the wrong resistance in a potential divider. The output is taken across R₂, so R₂ goes on top of the fraction.
• Saying a higher resistance gives a brighter lamp. In series, more resistance means less current and a dimmer lamp.

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