Gears of differing size are often used in pairs for a mechanical advantage, allowing the torque of the driving gear to produce a larger torque in the driven gear at lower speed, or a smaller torque at higher speed. The larger gear is known as a wheel and the smaller as a pinion. This is the principle of the automobile transmission, allowing selection between various mechanical advantages.
A gearbox is not an amplifier or a servomechanism. Conservation of energy requires that the amount of power delivered by the output gear or shaft will never exceed the power applied to the input gear, regardless of the gear ratio. Work equals the product of force and distance, therefore the small gear is required to run a longer distance and in the process is able to exert a larger twisting force or torque, than would have been the case if the gears were the same size. There is actually some loss of output power due to friction.
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