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Analog fuel gauges use a heated bimetal strip to move the indicator needle on the fuel gauge. The amount of current flowing through the gauge heats up the bimetal strip. The strip expands and determines how far the needle moves. Voltage is supplied to the gauge by a small voltage regulator in the instrument panel which reduces circuit voltage to about five volts.
The amount of current that flows through the fuel gauge is controlled by the ground circuit provided by the sending unit in the fuel tank. As the fuel level inside the tank goes up and down, the hinged arm that's attached to the float rotates a rheostat. This changes the amount of resistance in the ground circuit which allows more or less current to flow through the gauge.