5) Old-style dimmers consisted of a variable resistor so you could dial in more resistance to lower the current and, hence, dim the light. If the increased total resistance caused the current to be reduced by 50%, then by what percent would the power dissipation be reduced

The power of the bulb is reduced to a quarter

Explanation:

The power in an electrical circuit is

         P = V I = I² R

If the dimmer cuts the current in half

        I = I₀ / 2

The resistance of the light bulb after hot is little affected by small changes in the current

We substitute in the equation

       P = I₂ R

       P = (I₀ /2)² R

      P = ¼ I₀² R

      P = ¼ P₀

The power of the bulb is reduced to a quarter