Metal Resistance and Temperature Coefficient
Near a reference temperature T0 and over the stated linear range, R(T) = R0[1 + alpha(T-T0)]. Alpha belongs to the chosen reference convention and is not universally constant over large ranges.
Why this shows up in the exam
Resistance thermometers · Hot-filament estimates · Temperature correction of wire resistance
Learn the idea
Over a limited range, a metal's resistance is approximately linear in temperature. Hotter metal ions vibrate more and scatter conduction electrons more strongly, so ordinary metallic resistance usually rises with temperature.
🧠 Memory hook: For ordinary metals: hotter lattice, more scattering, larger R.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- R_T = R₀[1 + alpha(T-T₀)] — linear approximation near reference T0
- alpha = (R_T-R₀)/(R₀ Delta T) — temperature coefficient under that approximation
How to approach it
- 1Identify the reference resistance and temperature
- 2Use Delta T consistently
- 3Check whether a linear model is stated or reasonable
Common slip-ups that cost marks
- •Using Celsius temperature instead of temperature difference incorrectly
- •Applying one alpha over an extreme range
- •Assuming the same sign for semiconductors
🌟 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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