The Old Way
Early dimmer switches had a pretty straightforward solution to adjusting light levels -- a variable resistor. An ordinary resistor is a piece of material that doesn't conduct electrical current well -- it offers a lot of resistance to moving electrical charge. A variable resistor consists of a piece of resistive material, a stationary contact arm and a moving contact arm.
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In this design, you vary the total resistance of the resistor by adjusting the distance that the charge has to travel through resistive material. If the contact arm is to the left, charge flowing through the circuit only has to travel through a little bit of resistive material. If the contact arm is all the way to the right, the charge has to move through more resistive material.
As the charge works to move through the resistor, energy is lost in the form of heat. When you put a resistor in a series circuit, the resistor's energy consumption causes a voltage drop in the circuit, decreasing the energy available to other loads (the light bulb, for example). Decreased voltage across the light bulb reduces its light output.
The problem with this solution is that you end up using a lot of energy to heat the resistor, which doesn't help you light up the room but still costs you. In addition to be being inefficient, these switches tend to be cumbersome and potentially dangerous, since the variable resistor releases a substantial amount of heat.
Modern dimmer switches take a more efficient approach, as we'll see in the next section.