The fuel gauge on a car consists of three main parts they are the sender unit, the voltage regulator and the gauge itself.

The Sender Unit

The purpose of the sender unit is to measure the level of the fuel in the fuel. All sender units use a float that rises and falls with the level in the tank. This float is connected mechanically to an electrical device known as a variable resistor. Variable resistors can be found in many other electrical such as volume controls and household dimmer switches.

The Fuel Gauge

The fuel gauge itself operates on heat. Inside the gauge is a small piece of bimetallic material that is connected to the needle. Wrapped around this strip is some thin wire which gets warm when electrical current flows through it. This material is created using two different metals bonded together. These metals expand at different rates when they are heated. This causes the material to bend as one metal expands to a greater length than the other.

Operation

If you think of the system in relation to a household dimmer switch you can begin to see how the whole system operates. When the dimmer switch is in a low position the light is very dim and not much heat is generated. When the bimetallic strip is cool the needle will be in the empty position. However as the light switch is adjusted the brightness will increase, generating more heat. In the fuel gauges this is causes the bimetalic strip to deflect to a greater extend and the needle to move further toward the full position.

The Voltage Regulator

When a car is sat still, without the engine running and just the ignition switch on, the voltage measured at the terminals of the battery will be approximately 12V. However when the engine is started this will rise to about 13.6 volts. If it weren't for the voltage regulator this would cause the needle to move since the current flowing through the fuel gauge circuit would rise causing the temperature of the bimetallic strip to rise.

How stuff works
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Fundamentals of Motor Vehicle Technology
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