THE PRACTICE STUDIO
Go slowly. Ask why. Make it yours.
PRACTICE / Resistance and resistivity
Stretching changes two dimensions
A uniform wire has resistance 5 Ω. It is stretched to twice its length without changing volume, resistivity or temperature.
Find its new resistance.
Organize the givens & assumptions
- Rinitial = 5 Ω
- Lfinal = 2Linitial
- volume fixed
Uniform ohmic wire; stretch keeps volume, resistivity and temperature fixed; no damage effects.
Study with a tutor prompt
Copy this into your AI assistant, then describe where you got stuck. It asks the tutor to coach you one step at a time. Check its reasoning against the lesson.
Opening this prompt marks this practice attempt as assisted.
Problem: Stretching changes two dimensions A uniform wire has resistance 5 Ω. It is stretched to twice its length without changing volume, resistivity or temperature. Question: Find its new resistance. Givens: - Rinitial = 5 Ω - Lfinal = 2Linitial - volume fixed Assumptions: Uniform ohmic wire; stretch keeps volume, resistivity and temperature fixed; no damage effects. Choices (LaTeX): A. 20\ \Omega B. 10\ \Omega C. 5\ \Omega D. 2.5\ \Omega Ask for my approach first. Help me distinguish a physical misconception from an algebra error without revealing which choice is correct. Tutoring approach: Act as a patient physics tutor. Ask what I understand and what I have tried, then wait for my reply. Teach one step at a time; do not give the final answer or a complete solution immediately. Start with a physical picture. Define unfamiliar symbols and operators, explain signs and units, and state the model's assumptions. Give progressively stronger hints only when I need them. Ask me to predict a change before calculating it. When I finish, help me check dimensions and a limiting case, then ask one related transfer question. If information is missing or ambiguous, ask rather than inventing it. Distinguish exact results from approximations and acknowledge uncertainty.
Start with the smallest hint.
Work through it with me.
One decision at a time. Pause, predict, then unpack the algebra.
The longer path doubles resistance and the halved area doubles it again.
Choose a physical relation
Stretching lengthens the current path and reduces its cross section, both of which increase resistance.
Isolate what is asked
The longer path doubles resistance and the halved area doubles it again.
Why is this step valid?
Doubling length halves area at fixed volume, producing a resistance factor 2/(1/2).
Substitute and interpret
Resistance becomes 20 Ω, four times its original value; keeping area fixed would miss half the geometric change.
Writing resistance in terms of fixed material volume confirms the square dependence.
TRY THE IDEA AGAIN
If length triples under the same assumptions, what is the resistance factor?
YOUR LEARNING NOTE
How does this idea feel now?
Confidence is a reflection, not proof of mastery.
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