Stretching, Recasting, and Cutting Wires
If material, temperature, and volume AL are unchanged, A is inversely proportional to L and R = rho L squared divided by volume. Cutting changes each piece resistance before any reconnection.
Why this shows up in the exam
Stretched metal wires · Recast conductors · Cut-and-reconnect resistance changes
Learn the idea
When a wire is reshaped without material loss, volume conservation couples its new length and area. Stretching a wire does two things at once: it lengthens the path and thins the cross-section. That is why resistance can scale as the square of length when volume and resistivity stay fixed.
🧠 Memory hook: Stretch by k at fixed volume, resistance grows by k squared.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- A₁ L₁ = A₂ L₂ — volume conservation for uniform reshaping
- R₂/R₁ = (L₂/L₁)² — same material, temperature, and volume
- R_piece = R/n — n equal cuts along the original length
How to approach it
- 1Translate the physical operation
- 2Find each new piece resistance
- 3Only then apply series or parallel rules
Common slip-ups that cost marks
- •Keeping area unchanged while invoking volume conservation
- •Using the square law when resistivity changes
- •Forgetting to reconnect cut pieces as stated
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
A cell of emf 6 V and internal resistance 1 ohm is connected to a 2 ohm resistor. Find the circuit current.
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