Formula
Resistivity
R = ρ L / A, where ρ is resistivity (Ω·m). Conductivity σ = 1/ρ. Resistivity depends on material and temperature.
-- NCERT Class 12 Physics, Ch. 3, p. 84Resistivity Conductivity
8 MCQs1 revision card9-step worked example
Source: NCERT Current ElectricityPYQ coverage: NEET 2022Official key: NTA-verifiedLast updated: 21 Sep 2026
Resistivity Conductivity, explained for NEET
The common confusion: resistance and resistivity are not the same quantity. Resistance R belongs to a particular piece of wire. Resistivity ρ belongs to the material. Change the wire's length or thickness and R changes; ρ does not.
NCERT Class 12 Physics Chapter 3 (page 84, Eq 3.10) writes the link as:
R = ρL/A
So R is proportional to length L and inversely proportional to cross-sectional area A. Rearranging, ρ = RA/L, which gives the SI unit ohm metre (Ω m). Per the chapter summary, ρ depends on the material and on its temperature and pressure — not on the sample's dimensions. For metals, NCERT (page 90) gives resistivities in the range 10⁻⁸ to 10⁻⁶ Ω m.
Conductivity is the reciprocal: σ = 1/ρ, with unit (Ω m)⁻¹. NCERT (page 85, Eq 3.13) uses it in the microscopic form of Ohm's law, j = σE, where j is current density and E the electric field.
The microscopic picture (NCERT page 87, Eq 3.23, and page 91, Eq 3.27) connects σ to the electrons:
σ = ne²τ/m, so ρ = m/(ne²τ)
where n is the free-electron number density and τ the average relaxation time. Larger n or longer τ means higher conductivity and lower resistivity.
How NEET uses this: ratio questions. Two wires of the same material have the same ρ, so R ∝ L/A. With a circular wire, A ∝ d², so halving the diameter makes R four times larger, not two.
Watch out — stretching a wire. When a wire is drawn out uniformly, its volume LA stays fixed. Doubling L halves A, so R becomes 4 times, while ρ stays unchanged. Also convert areas carefully: 1 mm² = 10⁻⁶ m², not 10⁻³ m².
Can you answer these Resistivity Conductivity MCQs?
Select an option to see the explanation. Wrong answers show why your choice was tempting — and name the exact trap it exploits.
MCQ 1Easy RecallPractice
What is the SI unit of electrical resistivity?
Show answer and why every option is right or wrong
Answer: A. From R = ρL/A, ρ = RA/L, whose unit is Ω × m² / m = Ω m (NCERT Class 12 Physics Chapter 3, page 84).
Why B is wrong: B is wrong because the ohm is the unit of resistance R, a property of a specific wire. This is the resistance-versus-resistivity confusion.
Why C is wrong: C is wrong because Ω/m comes from dividing resistance by length and forgetting the area factor; ρ = RA/L carries m²/m = m in the numerator.
Why D is wrong: D is wrong because Ω m² keeps the area unit but forgets to divide by the length L in ρ = RA/L.
MCQ 2Easy RecallPractice
Which relation correctly gives the electrical conductivity σ of a material of resistivity ρ?
Show answer and why every option is right or wrong
Answer: D. Conductivity is the reciprocal of resistivity, σ = 1/ρ (NCERT Class 12 Physics Chapter 3, page 85).
Why A is wrong: A is wrong because RA/L is the expression for resistivity ρ itself, not its reciprocal.
Why B is wrong: B is wrong because 1/R is the reciprocal of resistance of a particular wire; conductivity is a material property and is the reciprocal of resistivity, not of resistance.
Why C is wrong: C is wrong because ρL/A is the resistance R of a wire, not conductivity.
MCQ 3Easy RecallPractice
The resistivity of a metallic conductor depends on:
Show answer and why every option is right or wrong
Answer: D. Resistivity is a material property; NCERT's chapter summary states it depends on the material and on temperature and pressure, not on the dimensions of the sample (NCERT Class 12 Physics Chapter 3).
Why A is wrong: A is wrong because length changes the resistance R = ρL/A, not the resistivity ρ. This mixes up resistance with resistivity.
Why B is wrong: B is wrong because area changes the resistance R, not the resistivity of the material. This is the resistance-versus-resistivity confusion.
Why C is wrong: C is wrong because both length and area are geometric factors that set R for a given sample; ρ is the same for any sample of the same material at the same temperature.
MCQ 4Direct ApplicationPractice
A wire of length 2.0 m and cross-sectional area 1.0 mm² is made of a material of resistivity 1.7 × 10⁻⁸ Ω m. What is its resistance?
Show answer and why every option is right or wrong
Answer: B. A = 1.0 mm² = 1.0 × 10⁻⁶ m². R = ρL/A = (1.7 × 10⁻⁸ × 2.0)/(1.0 × 10⁻⁶) = 3.4 × 10⁻² Ω (NCERT Class 12 Physics Chapter 3, page 84).
Why A is wrong: A is wrong because it uses the area as 1.0 m² — the mm² value was never converted to m² (1 mm² = 10⁻⁶ m²).
Why C is wrong: C is wrong because it divides ρ by both L and A, i.e. ρ/(LA) = 1.7 × 10⁻⁸/(2.0 × 10⁻⁶); resistance is proportional to length, so L belongs in the numerator.
Why D is wrong: D is wrong because it converts 1.0 mm² as 10⁻³ m², using the length conversion factor instead of squaring it.
MCQ 5Direct ApplicationPractice
Wires P and Q are made of the same material. Q has twice the length and twice the diameter of P. What is the ratio R_Q/R_P of their resistances?
Show answer and why every option is right or wrong
Answer: A. Same material, so ρ is the same and R ∝ L/A ∝ L/d². R_Q/R_P = 2/(2)² = 2/4 = 1/2 (NCERT Class 12 Physics Chapter 3, page 84).
Why B is wrong: B is wrong because it takes area proportional to diameter (2/2 = 1); area of a circular section goes as d², so doubling d makes A four times larger.
Why C is wrong: C is wrong because it multiplies by the area factor (2 × 4 = 8) instead of dividing by it; R is inversely proportional to A.
Why D is wrong: D is wrong because it accounts for the doubled length but ignores the change in cross-sectional area altogether.
MCQ 6Direct ApplicationPractice
A material has resistivity 2.5 × 10⁻⁸ Ω m. What is its conductivity?
Show answer and why every option is right or wrong
Answer: C. σ = 1/ρ = 1/(2.5 × 10⁻⁸) = 0.40 × 10⁸ = 4.0 × 10⁷ (Ω m)⁻¹ (NCERT Class 12 Physics Chapter 3, page 85).
Why A is wrong: A is wrong because it simply rewrites the resistivity value with the conductivity unit, without taking the reciprocal.
Why B is wrong: B is wrong because it gets the number right (1/2.5 = 0.40, i.e. 4.0) but gives the power of ten the wrong sign; the reciprocal of 10⁻⁸ is 10⁺⁸, so the answer is 4.0 × 10⁺⁷, not 4.0 × 10⁻⁷.
Why D is wrong: D is wrong because it flips the sign of the exponent but does not take the reciprocal of 2.5; 1/2.5 = 0.40, giving 4.0 × 10⁷.
MCQ 7CalculationPractice
A uniform wire of resistance R and resistivity ρ is stretched uniformly to twice its original length, its volume remaining unchanged. What are its new resistance and new resistivity?
Show answer and why every option is right or wrong
Answer: C. Volume LA is constant, so L → 2L gives A → A/2. R' = ρ(2L)/(A/2) = 4ρL/A = 4R. The material is unchanged, so resistivity stays ρ (NCERT Class 12 Physics Chapter 3, page 84).
Why A is wrong: A is wrong because the resistance does become 4R, but resistivity is a material property and does not change when the wire's shape changes.
Why B is wrong: B is wrong because it doubles R for the doubled length but forgets that the cross-sectional area halves at constant volume, which doubles R again.
Why D is wrong: D is wrong because it forgets the area reduction (giving 2R) and also treats resistivity as if it depended on the wire's length.
MCQ 8Concept TrapPractice
In a conductor, suppose the average relaxation time τ of the free electrons doubled while the electron number density n stayed the same. The resistivity would:
Show answer and why every option is right or wrong
Answer: B. ρ = m/(ne²τ), so ρ ∝ 1/τ at fixed n. Doubling τ halves ρ (NCERT Class 12 Physics Chapter 3, page 91).
Why A is wrong: A is wrong because it treats ρ as proportional to τ; that is the behaviour of conductivity σ = ne²τ/m, not resistivity.
Why C is wrong: C is wrong because it assumes resistivity is fixed by the material label alone; ρ = m/(ne²τ) shows it changes with the microscopic quantities n and τ.
Why D is wrong: D is wrong because it treats ρ as proportional to 1/τ², squaring τ; in ρ = m/(ne²τ) it is the charge e that is squared, not τ.
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Resistivity Conductivity: quick recall before you leave
How do you solve a Resistivity Conductivity question? A worked example
- 1
Given
A uniform metal wire has length L = 0.40 m, diameter d = 0.50 mm = 5.0 × 10⁻⁴ m, and measured resistance R = 2.0 Ω.
- 2
Required
Find the resistivity ρ and the conductivity σ of the material.
- 3
Concept
Resistance depends on the material through ρ and on geometry through L/A. Rearranging R = ρL/A isolates the material property. Conductivity is the reciprocal of resistivity.
- 4
Formula
R = ρL/A, so ρ = RA/L; A = πd²/4; σ = 1/ρ
- 5
Substitution
A = π × (5.0 × 10⁻⁴ m)² / 4
ρ = (2.0 Ω × A) / (0.40 m) - 6
Calculation
A = π × 2.5 × 10⁻⁷ / 4 = 1.963 × 10⁻⁷ m²
ρ = (2.0 × 1.963 × 10⁻⁷) / 0.40 = 9.82 × 10⁻⁷ Ω m
σ = 1 / (9.82 × 10⁻⁷) = 1.02 × 10⁶ (Ω m)⁻¹
The factor 4 in A = πd²/4 and the constant π are exact and do not contribute to the significant-figure count; the data (0.40 m, 0.50 mm, 2.0 Ω) each have 2 significant figures. - 7
Final answer
ρ ≈ 9.8 × 10⁻⁷ Ω m and σ ≈ 1.0 × 10⁶ (Ω m)⁻¹ (2 significant figures). This lies inside NCERT's range for metals, 10⁻⁸ to 10⁻⁶ Ω m.
- 8
Common trap
Two slips are frequent here: using the diameter in place of the radius without the factor 4 (A = πd², which makes ρ four times too large), and leaving d in millimetres (which gives an area 10⁶ times too large). A third is to report the resistance 2.0 Ω as if it were the resistivity.
- 9
Similar NEET-style question
"A wire of the same material as above has length 0.80 m and diameter 0.25 mm. What is its resistance?"
Strategy: Same material, so ρ is unchanged and R ∝ L/d². Length doubles (×2) and diameter halves (area ×1/4, so R ×4). R = 2.0 Ω × 2 × 4 = 16 Ω.
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What to remember before solving Resistivity Conductivity questions
Which Resistivity Conductivity formulas do you need for NEET?
1 formula — click to collapse
Resistivity formula
Resistance from material resistivity, length, cross-sectional area.
| Symbol | Quantity | SI Unit |
|---|---|---|
| R | resistance | Ω |
| rho | resistivity | Ω*m |
| L | length | m |
| A | area | m^2 |
Valid when
- Uniform conductor
- Steady current
More in Current Electricity: 3 exam traps and mistakes · 6 formulas · 6 question patterns from its other lessons.
Resistivity Conductivity questions from past NEET papers
1 question from NEET 2022. Answers verified against NTA official keys. — click to collapse
NEET 2022
110⁵ A/m²
210⁴ A/m²
310⁶ A/m²
410⁻⁵ A/m²
NTA Answer: Option 1(final)
Sources
Page numbers are the ones printed in the current NCERT textbook (2023 rationalised edition), unless marked pre-2023. The books are free at ncert.nic.in.
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