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

no. dot product   =0 when vecs at right angles

as we know our atmosphere or air have different levels. every level has other gasses, and every gas has another permeability. when the light comes from lower permeability to higher permeability, it changes its direction. so that means that when the light comes from the moon to the earth, it changes it's direction many more times. it basically means that the shape of the light part of the moon is changed on the earth.

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