# Creating a Variable Resistor Using a Bare Resistance Wire and Sliding Contact

In summary, a dopey resistance question is a sarcastic or dismissive question that does not contribute to productive discourse. People may ask these types of questions to discredit or deflect attention from topics they do not agree with. The best way to respond to a dopey resistance question is to remain calm, present factual evidence, and maintain a respectful tone. In most cases, there is little to no value in asking these questions as they do not promote critical thinking or understanding. To avoid asking dopey resistance questions, it is important to approach discussions with an open mind, avoid dismissing ideas without consideration, and ask genuine and thoughtful questions.
You have a length of bare resistance wire a fixed contact and a sliding contact.Using these things only how can you make a variable resistor such that when the sliding contact is moved along the wire the resistance varies smoothly from zero to a maximum and then to zero?You are not allowed to cut the wire.

Form the wire (of length L and resistance R) into a closed loop. If the sliding contact is at a distance d from the fixed contact, the resistance will be the equivalent parallel resistance from segments of length d and L-d, which should be:

R_eff = [R(d/L)*R((L-d)/L)]/[R(d/L)+R((L-d)/L)] = Rd(L-d)/(L^2),

and as d increases from 0, d(L-d) increases smoothly from 0 till d=L/2 (where R_eff is at its maximal value of R/4) and decreases smoothly to 0 after that (this part maps onto the common puzzle of maximizing the area of a rectangle of given perimeter, but if you don't like that, then the first derivative is L-2d, and the second is -2).

Well done Gokul 43201.

## 1. What is a dopey resistance question?

A dopey resistance question is a question that is asked without any intention of gaining knowledge or understanding. It is often asked in a sarcastic or dismissive manner, and does not contribute to productive discourse.

## 2. Why do people ask dopey resistance questions?

People may ask dopey resistance questions as a way to discredit or dismiss an argument or idea that they do not agree with. It can also be used as a means of deflecting attention away from a topic they do not want to address.

## 3. How should one respond to a dopey resistance question?

The best way to respond to a dopey resistance question is to remain calm and address the question with factual evidence and reasoning. It is important to not engage in a heated argument and to maintain a respectful tone.

## 4. Is there any value in asking dopey resistance questions?

In most cases, there is little to no value in asking dopey resistance questions. They do not contribute to productive discussions and can often hinder progress and understanding. It is important to ask genuine and thoughtful questions in order to gain knowledge and promote critical thinking.

## 5. How can we avoid asking dopey resistance questions?

The best way to avoid asking dopey resistance questions is to approach discussions with an open mind and a willingness to listen and learn. It is important to avoid dismissing ideas or arguments without considering them first. It is also helpful to think before speaking and to ask genuine questions that contribute to the conversation.

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