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Chapter 7 Review Exercises

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.

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    • 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.

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    • 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.

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    • 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.

      data folder

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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?

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    • 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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