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### Chapter 7 Review Exercises

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• 1. Temperature and Resistance

The table shows the resistances of a coil of copper wire at various temperatures. Does the table relating temperature and resistance represent a linear pattern? Explain your reasoning.

• Worked-Out Solution

Use a spreadsheet to analyze the data in the table.

The data does represent a linear pattern because the first differences are equal.

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```  ______    _____     _____    _    _    __   __
/_   _//  |  ___||  |__  //  | || | ||  \ \\/ //
`-| |,-   | ||__      / //   | || | ||   \   //
| ||    | ||__     / //__  | \\_/ ||   / . \\
|_||    |_____||  /_____||  \____//   /_//\_\\
`-`'    `-----`   `-----`    `---`    `-`  --`

```
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• 2. Temperature and Resistance

The table shows the resistances of a coil of copper wire at various temperatures. Use a spreadsheet to graph the data. Is the graph linear?

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```__    __   __   __   ______      ___     ______
\ \\ / //  \ \\/ // |      \\   / _ \\  |      \\
\ \/ //    \ ` //  |  --  //  / //\ \\ |  --  //
\  //      | ||   |  --  \\ |  ___  |||  --  \\
\//       |_||   |______// |_||  |_|||______//
`        `-`'   `------`  `-`   `-` `------`

```
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• 3. Temperature and Resistance

The table shows the resistances of a coil of copper wire at various temperatures. Find the resistance of the coil when the temperature is 30°C.

• Worked-Out Solution

Extend the spreadsheet to a temperature of 30 degrees Celsius. The resistance is 103.8 ohms.

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```           __   __    _  __    _____     ______
___    \ \\/ //  | |/ //  |  ___||  /_   _//
/   ||   \ ` //   | ' //   | ||__      | ||
| [] ||    | ||    | . \\   | ||__     _| ||
\__ ||    |_||    |_|\_\\  |_____||  /__//
-|_||    `-`'    `-` --`  `-----`   `--`
`-`
```
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• 4. Temperature and Resistance

The table shows the resistances of a coil of copper wire at various temperatures. Find the resistance of the coil when the temperature is 48°C.

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```  ______     ___      ____      _____    _    _
/_____//   / _ \\   |  _ \\   |  ___|| | || | ||
`____ `   | / \ ||  | |_| ||  | ||__   | || | ||
/___//    | \_/ ||  | .  //   | ||__   | \\_/ ||
`__ `      \___//   |_|\_\\   |_____||  \____//
/_//       `---`    `-` --`   `-----`    `---`
`-`
```
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• 5. Length and Resistance

The table shows the resistances of a coil of copper wire for various lengths. Is the length of the wire proportional to its resistance? Make a scatter plot of the data to verify your answer.

• Worked-Out Solution

Because the resistance is 0.017 times the length of the wire, the resistance of the wire is proportional to the length of the wire. Use a spreadsheet to make a scatter plot of the data.

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```            ______    _  _     _____
____     /_   _//  | \| ||  |  ___||     ___
|    \\    -| ||-   |  ' ||  | ||__      /   ||
| [] ||    _| ||_   | .  ||  | ||__     | [] ||
|  __//   /_____//  |_|\_||  |_____||    \__ ||
|_|`-`    `-----`   `-` -`   `-----`      -|_||
`-`                                        `-`
```
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• 6. Length and Resistance

The table shows the resistances of a coil of copper wire for various lengths. Extend the pattern in the table to find the resistance for each length of the copper wire.

1. 26 meters
2. 28 meters
3. 30 meters

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```           __   __   ______      ___     _    _
____     \ \\/ // |      \\   / _ \\  | \  / ||
|    \\    \ ` //  |  --  //  | / \ || |  \/  ||
| [] ||     | ||   |  --  \\  | \_/ || | .  . ||
|  __//     |_||   |______//   \___//  |_|\/|_||
|_|`-`      `-`'   `------`    `---`   `-`  `-`
`-`
```
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• 7. Voltage and Current

Electric current is proportional to voltage.

Suppose a wire connected to a 3-volt battery has a current of 15 amperes. What is the current when the wire is connected to a 9-volt battery?

• Worked-Out Solution

Knowing that current is proportional to voltage and also knowing that a 3-volt battery has a current of 15 amps, you can make the following spreadsheet.

From the spreadsheet, you can see that a 9-volt battery has a current of 45 amps.

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``` _    _     ______   __   __     ___      _  _
| |  | ||  /_   _//  \ \\/ //   / _ \\   | \| ||
| |/\| ||   -| ||-    \   //   / //\ \\  |  ' ||
|  /\  ||   _| ||_    / . \\  |  ___  || | .  ||
|_// \_||  /_____//  /_//\_\\ |_||  |_|| |_|\_||
`-`   `-`  `-----`   `-`  --` `-`   `-`  `-` -`

```
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• 8. Voltage and Current

Electric current is proportional to voltage.

Suppose a wire connected to a 1.5-volt battery has a current of 20 amperes. What is the current when the wire is connected to a 4.5-volt battery?

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```  ____      _____              __   __    ______
|  _ \\   |  ___||   ____     \ \\/ //  /_   _//
| |_| ||  | ||__    |    \\    \ ` //   `-| |,-
| .  //   | ||__    | [] ||     | ||      | ||
|_|\_\\   |_____||  |  __//     |_||      |_||
`-` --`   `-----`   |_|`-`      `-`'      `-`'
`-`
```
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