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Chapter 44: Chapter 44

Problem 1243

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The resistance \(\mathrm{R}\) of a given size of wire at constant temperature varies directly as the length \(\ell\). It is found that the resistance of 100 feet of number 14 copper is \(0.253\) ohm. Construct a table of values for the given lengths of number 14 copper wire assuming the temperature is constant.

Short Answer

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Here is the table of resistance values for the given lengths of number 14 copper wire, assuming a constant temperature: Length (feet) | Resistance (ohms) --------------|------------------- 50 | 0.1265 100 | 0.253 150 | 0.3795 200 | 0.506 250 | 0.6325
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TABLE OF CONTENTS :
TABLE OF CONTENTS

Step 1: Find the constant of variation k

Since the resistance R varies directly as the length l, there is a constant of variation k such that R = k * l. Given that the resistance of 100 feet of number 14 copper is 0.253 ohm, we can plug in the given values into the equation to find k: \(0.253 = k * 100\) Now, solving for k: \(k = \frac{0.253}{100} = 0.00253\)

Step 2: Calculate resistance for given lengths

Now that we have found k, we can use the formula R = k * l to calculate the resistance for any given length of number 14 copper wire. Let's assume we are given the following lengths to calculate the resistance: 50 feet, 100 feet, 150 feet, 200 feet, and 250 feet.

Step 3: Construct a table

We will now present our results in a table format. The table will have two columns: one for the length of wire in feet and the other for the resistance in ohms. Length (feet) | Resistance (ohms) --------------|------------------- 50 | \(\displaystyle 0.00253 * 50=0.1265\) 100 | \(\displaystyle 0.00253 * 100=0.253\) 150 | \(\displaystyle 0.00253 * 150=0.3795\) 200 | \(\displaystyle 0.00253 * 200=0.506\) 250 | \(\displaystyle 0.00253 * 250=0.6325\) The table above provides the resistance values for various lengths of number 14 copper wire at a constant temperature.

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