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Exam level7 past questions

Resistivity, Conductivity, and Material Properties

Learn how resistivity and conductivity depend on material, length, area, and how resistance changes with dimensions and temperature.

Why this shows up in the exam

You need to analyze how resistance varies with material and geometry, a common NEET question type.

How NEET tests this

Statement analysis · 3 QsApplication · 2 QsNumerical

Learn the idea

Resistivity (ρ) is the intrinsic opposition of a material to current; conductivity (σ) is its reciprocal. The resistance of a uniform wire is R = ρ L/A and changes with temperature as R = R₀(1+αΔt). The key insight is that geometry (L, A) and temperature (α) are separable factors that scale R linearly.

🧠 Memory hook: R = ρ L/A – think “Resistivity Loves Length, Avoids Area” (ρ L over A).

Get this one clearly and it pays off every single time it shows up in the paper. 🎯

Formulas & facts to keep ready

  • Resistivity ρ (Ω·m) is a material constant; conductivity σ = 1/ρ.
  • For a uniform conductor R = ρ L/A where L is length and A cross‑sectional area.
  • Temperature dependence for metals: R = R₀[1+α(t‑t₀)], α is the temperature coefficient at t₀ (usually 0 °C).
  • α is positive for metals and has units °C⁻¹.
  • If the temperature change is Δt, then ΔR = α R₀ Δt.
  • The same formula applies to resistivity: ρ_t = ρ₀(1+αΔt).

How to approach it

  1. 1Read the question and note which quantities are given (R, L, A, ρ, α, temperature).
  2. 2Choose the appropriate formula – geometry (R = ρ L/A) or temperature (R = R₀[1+αΔt]).
  3. 3Insert the numbers, keeping Δt = final − initial temperature; solve for the unknown (α, ρ, R, etc.).
  4. 4Check units and whether the answer is reasonable (order of magnitude).

Worked example — watch it click

The resistance of platinum wire at 0°C is 2Ω and 6.8Ω at 80°C. The temperature coefficient of resistance of the wire is

  • A)3 × 10⁻³ °C⁻¹
  • ✅3 × 10⁻² °C⁻¹
  • C)3 × 10⁻¹ °C⁻¹
  • D)3 × 10⁻⁴ °C⁻¹

The concept behind this problem

The worked example asks for the temperature coefficient α, so you must apply the linear temperature‑dependence formula R = R₀(1+αΔt).

Step by step

  1. 1Using R_t = R₀(1 + αt): 6.8 = 2(1 + α×80).
  2. 2Solving: α = 4.8/(2×80) = 0.03 = 3 × 10⁻² °C⁻¹.

Watch out

Students often plug 80 °C directly instead of Δt = 80 °C (since t₀ = 0 °C), giving a wrong α.

Common slip-ups that cost marks

  • •Using the absolute temperature instead of the temperature difference Δt.
  • •Confusing α (°C⁻¹) with resistivity ρ (Ω·m) or mixing them up in the formula.
  • •Treating diameter as area directly – remember A = πd²/4.

🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.

Practise it

These are real questions from past NEET papers that test this exact idea.

Question 1 of 7NEET 2023

The resistance of platinum wire at 0°C is 2Ω and 6.8Ω at 80°C. The temperature coefficient of resistance of the wire is

Push further

More challenging

14 harder questions built from the past papers above — a step up in difficulty, with distractors designed so you can't get there by elimination. Written and checked by our reviewers, not from a real paper.

Question 1 of 14

Consider two materials: a copper wire and a dilute aqueous solution of NaCl. Which of the following statements accurately compares their electrical conductivities at a given temperature?

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