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

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

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

```
• 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.

These comments are not screened before publication. Constructive debate about the information on this page is welcome, but personal attacks are not. Please do not post comments that are commercial in nature or that violate copyright. Comments that we regard as obscene, defamatory, or intended to incite violence will be removed. If you find a comment offensive, you may flag it.

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

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

These comments are not screened before publication. Constructive debate about the information on this page is welcome, but personal attacks are not. Please do not post comments that are commercial in nature or that violate copyright. Comments that we regard as obscene, defamatory, or intended to incite violence will be removed. If you find a comment offensive, you may flag it.

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

```
• 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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