Why does a re-formed copper rod have a resistance of 4R instead of 2R?

• juggalomike
In summary, a cylindrical copper rod with length L and cross-sectional area A is re-formed to twice its original length with no change in volume. The resistance between its ends, originally R, is now 4R. This is because when the length is doubled, the cross-sectional area is halved, leading to a four-fold increase in resistance.
juggalomike

Homework Statement

A cylindrical copper rod of length L and cross-sectional area A is re-formed to
twice its original length with no change in volume. If the resistance between its
ends was originally R, what is it now?

R=p(L/A)

The Attempt at a Solution

Using the above equation the answer would be 2R, however the correct answer is 4R. Why is this? I am studying for a test tomorrow and need to understand why this is so.

If it has the same volume but twice the length, what will happen to the cross-sectional area?

alex3 said:
If it has the same volume but twice the length, what will happen to the cross-sectional area?

ahhh, it will be 1/2 of the original, thanks.

1. What is resistance?

Resistance is a measure of how much a material or object impedes the flow of electric current. It is typically represented by the symbol "R" and is measured in ohms (Ω).

2. How is resistance calculated?

Resistance is calculated using Ohm's Law, which states that resistance is equal to voltage (V) divided by current (I). This can be represented by the equation R = V/I.

3. What factors affect resistance?

Resistance is affected by several factors, including the type of material, its length and cross-sectional area, and its temperature. In general, materials with higher resistivity, longer length, and smaller cross-sectional area will have higher resistance.

4. Why is resistance important?

Resistance is important because it is a fundamental property of materials and is necessary for the proper functioning of many electronic devices. It also plays a crucial role in determining the amount of current that flows through a circuit.

5. What are some practical applications of resistance?

Resistance has many practical applications, including in electronic circuits, heating elements, and sensors. It is also used in resistors, which are components that are specifically designed to limit the flow of current in a circuit.

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