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Problem 1243

# 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.

Expert verified
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
See the step by step solution

## 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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