Chapter 7: Problem 13

A solid metal cylinder has a certain resistance. It is then heated and carefully stretched to form a longer, thinner cylinder. After it cools, will its resistance be the same as, greater than, or less than what it was before?

Short Answer

Expert verified

Answer: The resistance will be greater than what it was before.

Step by step solution

Identify given information and variables

We have a metal cylinder with a known resistance. When heated and stretched, it changes its length (L) and cross-sectional area (A). We need to determine the effect of these changes on the resistance (R). Resistivity (ρ) is a constant for a given material and will not be affected by the changes in dimensions.

Analyze the change in dimensions

When the cylinder is heated and stretched, its length (L) increases and cross-sectional area (A) decreases. Since the volume of a cylinder remains constant through this process, we can use the formula for the volume of a cylinder, which is given by: Volume (V) = Length (L) × Cross-sectional Area (A) The volume remains constant, so the product of L and A remains the same before and after stretching the cylinder.

Use the resistance formula to find the change in resistance

The formula for resistance (R) is: Resistance (R) = Resistivity (ρ) × Length (L) / Cross-sectional Area (A) As the length (L) increases and cross-sectional area (A) decreases (with a constant product), the ratio L/A will increase. Since the resistivity (ρ) stays constant and the ratio L/A increases, the resistance (R) will also increase.

Compare the resistance values before and after stretching

Since the resistance (R) increases due to the change in dimensions, we can conclude that the resistance after stretching and cooling will be greater than what it was before. So, the answer to the problem is that the resistance will be greater than what it was before.

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A solid metal cylinder has a certain resistance. It is then heated and carefully stretched to form a longer, thinner cylinder. After it cools, will its resistance be the same as, greater than, or less than what it was before?

Short Answer

Step by step solution

Identify given information and variables

Analyze the change in dimensions

Use the resistance formula to find the change in resistance

Compare the resistance values before and after stretching

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