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# Inverse Variation Models

## Identify and solve y=k/x form equations

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Practice Inverse Variation Models

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Bump in the Night

You?re startled awake at 3 a.m. by a noise in the kitchen. Curious about what the noise could be, you tiptoe out of bed, down the stairs, through the dark hallway, and to the doorway of the kitchen. You can?t see anything, but you definitely hear a rustling. You know that to the right of the doorway is the light switch for the kitchen. You hit the switch, and since the kitchen lights are on a dimmer, the lights gradually turn on until they reach full brightness?and now you see the culprit. Your dog turns and looks at you with a guilty look on his face, as he continues to eat the remains of the pot roast from dinner that were in the trash but are now spread across the kitchen floor.

#### News You Can Use

The dimmer switch controlling your kitchen lights works because of Ohm?s Law. A dimmer switch is a variable resistor. In other words, the electrical resistance of the circuit decreases as the light increases in brightness; on the other hand, the resistance of the circuit increases as the light decreases in brightness.

Ohm?s Law states that the flow of electric current is directly proportional to the voltage and inversely proportional to the resistance. In the case of the dimmer switch, the voltage coming into the switch is always the same, but the light switch controls the resistance of the circuit. As you adjust the dimness or brightness of the light to your preference, the switch increases or decreases the resistance accordingly.

See for yourself: http://www.physicsclassroom.com/class/circuits/u9l3c.cfm

#### Explore More

If the resistance of a circuit were tripled, while the voltage stayed the same, what would happen to the current through the circuit?

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