Temperature Coefficient of Resistance: Meaning and Sign
Physics · Current Electricity · NEET
The temperature coefficient of resistance, alpha (α), tells you the fractional change in resistance per degree Celsius rise in temperature: R = R0[1 + α(T − T0)]. It is POSITIVE for metals (resistance rises when heated) and NEGATIVE for semiconductors and insulators (resistance falls when heated). Memory hook: "Metals get lazy when hot (α+), semiconductors wake up when hot (α−)."
Left: a metal has positive alpha, so resistance rises almost linearly with temperature (more electron scattering). Right: a semiconductor has negative alpha, so resistance falls as temperature rises (more free carriers). The sign of alpha is what NEET tests most.
Your doubts, answered
What exactly does the temperature coefficient of resistance mean?
Alpha (α) is the fractional change in resistance for each 1 degree Celsius rise in temperature. From R = R0[1 + α(T − T0)], rearrange to get α = (R − R0) / (R0 × ΔT). So if α = 0.004 per degree C, the resistance goes up by 0.4% for every 1 degree C rise. It is a property of the material, measured from a reference temperature T0 (usually 0 degree C or 20 degree C).
Is alpha positive or negative? How do I decide the sign for NEET?
For METALS (copper, platinum, tungsten, nichrome) alpha is POSITIVE: heating adds more lattice vibrations, electrons scatter more, so resistance rises. For SEMICONDUCTORS and INSULATORS (silicon, germanium, carbon) alpha is NEGATIVE: heating frees more charge carriers, so resistance falls. NEET loves this one line: metals α positive, semiconductors and insulators α negative.
Why is alpha negative for semiconductors when metals go positive?
In a metal the number of free electrons barely changes with temperature; heating only increases collisions (scattering), so resistance goes up. In a semiconductor, heating jumps many extra electrons across the energy gap into conduction. This huge rise in carrier number beats the extra scattering, so overall resistance drops. More carriers win, so alpha comes out negative.
What is the unit and dimension of the temperature coefficient of resistance?
Alpha has the unit per degree Celsius (°C⁻¹) or equivalently per kelvin (K⁻¹). Its dimension is (Temperature)⁻¹ = [K⁻¹]. It is NOT dimensionless, even though the bracket (1 + α ΔT) is dimensionless, because α always multiplies a temperature difference.
Does the same alpha apply to resistance and to resistivity?
Yes, to a very good approximation. Resistance R = ρL/A, and for small heating the length and area change is tiny, so R and ρ change in almost the same ratio. NCERT defines α from resistivity: ρT = ρ0[1 + α(T − T0)], and NEET questions freely apply the same α to R. So R = R0[1 + α ΔT] and ρ = ρ0[1 + α ΔT] use the same α value.
⚠️ The NEET trap ✗ Alpha is negative for all non-metals, so insulators must have a positive coefficient like metals. ✓ Both semiconductors AND insulators have a NEGATIVE temperature coefficient (their resistance falls when heated). Only metals have positive alpha. 🧠 NEET 2020 asked exactly this: the correct answer was 'insulators and semiconductors', not 'semiconductors only'. Do not leave insulators out.
Real NEET questions
NEET 2023
The resistance of a platinum wire is 2 Ω at 0°C and 6.8 Ω at 80°C. The temperature coefficient of resistance is:
A · 3 × 10⁻⁴ °C⁻¹
B · 3 × 10⁻³ °C⁻¹
C · 3 × 10⁻² °C⁻¹ ✓
D · 3 × 10⁻¹ °C⁻¹
Solution: Use α = (R − R0) / (R0 × ΔT). Here R0 = 2 Ω at 0°C, R = 6.8 Ω at 80°C, so ΔT = 80°C. Step 1: R − R0 = 6.8 − 2 = 4.8 Ω. Step 2: R0 × ΔT = 2 × 80 = 160. Step 3: α = 4.8 / 160 = 0.03 = 3 × 10⁻² °C⁻¹. Answer: C.
NEET 2020
The solids which have the negative temperature coefficient of resistance are:
A · Semiconductors only
B · Insulators and semiconductors ✓
C · Metals
D · Insulators only
Solution: Negative α means resistance decreases as temperature rises. This happens when heating frees more charge carriers, which is true for BOTH semiconductors and insulators. Metals instead have positive α (more scattering when hot). So the answer is 'insulators and semiconductors', option B. Trap: do not pick 'semiconductors only' and forget insulators.
ReNEET 2026
Two circuits A and B each use two resistors, one with coefficient +α and one with −α, each R0 at the start. In A they are in series, in B in parallel, across the same battery. As temperature rises, which is correct?
A · I_A stays constant while I_B increases ✓
B · I_A decreases while I_B increases
C · I_A increases while I_B decreases
D · both stay constant
Solution: Series (A): R_eq = R0(1 + αΔT) + R0(1 − αΔT) = 2R0. The ±α terms cancel, so R_eq is independent of temperature and I_A = V/(2R0) stays constant. Parallel (B): R_eq = [R0(1 + αΔT) × R0(1 − αΔT)] / (2R0) = R0(1 − α²ΔT²)/2, which decreases as T rises, so I_B = V/R_eq increases. Answer: A.
Solved Current Electricity NEET PYQs
Try the real previous-year questions from this chapter — each with the answer and a full solution.
What is the formula for temperature coefficient of resistance?
R = R0[1 + α(T − T0)], which rearranges to α = (R − R0) / (R0 × ΔT), where R0 is the resistance at reference temperature T0 and ΔT = T − T0.
Is the temperature coefficient of resistance positive or negative for copper?
Copper is a metal, so its alpha is POSITIVE (about +3.9 × 10⁻³ °C⁻¹). Its resistance and resistivity increase almost linearly as temperature rises.
What is the unit of temperature coefficient of resistance?
Per degree Celsius (°C⁻¹) or per kelvin (K⁻¹). Its dimension is (Temperature)⁻¹, so it is not dimensionless.
Why does a semiconductor have a negative temperature coefficient?
Heating jumps many extra electrons into the conduction band. This large rise in carrier number lowers resistance faster than scattering raises it, so alpha is negative.
Is alpha the same for resistance and resistivity?
For small temperature changes, yes. NCERT defines α from resistivity, but since size changes are tiny, the same α is used for R = R0[1 + α ΔT] in NEET problems.
