Important Dimensions of Complete Physics – Complete Notes, Revision, Important Questions & Downloads
This topic compiles the dimensional formulae of physical quantities across two major branches: Heat and Thermodynamics Dimensions covers temperature [M⁰L⁰T⁰θ¹], heat energy [ML²T⁻²], specific heat [M⁰L²T⁻²θ⁻¹], Boltzmann constant [M¹L²T⁻²θ⁻¹], Stefan’s constant [M¹L⁰T⁻³θ⁻⁴], and Planck’s constant [M¹L²T⁻¹], while Electricity Dimensions covers charge [M⁰L⁰T¹A¹], capacitance [M⁻¹L⁻²T⁴A²], resistance [M¹L²T⁻³A⁻²], magnetic induction [M¹L⁰T⁻²A⁻¹], and permeability [M¹L¹T⁻²A⁻²]. NEET directly asks ‘find the dimensions of X’ for 1–2 questions per year from this chapter, often targeting Planck’s constant, Stefan’s constant, or permittivity of free space because their dimensional formulae involve four or more base quantities and are easy to confuse. For example, knowing that [h] = [M¹L²T⁻¹] immediately eliminates three distractors in a typical NEET MCQ.
NEET Weightage — Important Dimensions of Complete Physics
Units, Dimensions and Measurement (Chapter 1)| NEET Year | Questions from this Topic | Bar | Marks |
|---|---|---|---|
| 2024 | 1 | 4 | |
| 2023 | 2 | 8 | |
| 2022 | 1 | 4 | |
| 2021 | 1 | 4 | |
| 2020 | 1 | 4 | |
| 2019 | 1 | 4 | |
| 6-Year Total (2019–2024) | 5–8 | 20–32 |
Permittivity ε₀ [M⁻¹L⁻³T⁴A²] and permeability μ₀ [M¹L¹T⁻²A⁻²] are paired in NEET problems asking students to verify the dimension of c = 1/√(μ₀ε₀) — always decompose each constant separately.
Capacitance [M⁻¹L⁻²T⁴A²] and resistance [M¹L²T⁻³A⁻²] share no dimensional exponents, yet students frequently confuse them because both are electrical-circuit quantities — the sign of the M exponent distinguishes them instantly.
Exam Strategy for Important Dimensions of Complete Physics
Group dimensions by the number of base quantities involved Sort the table into 2-base-quantity (e.g., Heat [ML²T⁻²]), 3-base-quantity (e.g., specific heat [M⁰L²T⁻²θ⁻¹]), and 4-base-quantity entries (e.g., Stefan’s constant [M¹L⁰T⁻³θ⁻⁴]). NEET favours 4-base quantities because they generate the most plausible distractors. Memorise these first.
Derive rather than memorise wherever possible For each quantity, write its defining equation (e.g., σ = Power/(Area × T⁴)) and substitute known dimensions: [M¹L²T⁻³]/([L²][θ⁴]) = [M¹L⁰T⁻³θ⁻⁴]. Derivation cements recall; rote memorisation alone fails when NEET shuffles exponent signs.
Verify with dimensional checks on known equations Use energy = kT to confirm [k] = [ML²T⁻²]/[θ] = [M¹L²T⁻²θ⁻¹]. Use F = qE to confirm [E] = [MLT⁻²]/[AT] = [M¹L¹T⁻³A⁻¹]. If a derived dimension contradicts the table, re-derive — this catches sign and exponent errors before the exam.
Practise with elimination on 4-option MCQs When NEET gives four dimensional formulae, first check the mass exponent (positive vs negative vs zero), then the current exponent if present. Two checks typically eliminate three options. For example, capacitance has M⁻¹ — any option with M¹ is wrong immediately.
Download Study Notes — Important Dimensions of Complete Physics
PDF · Cheat Sheet · MCQ Set · PYQSubtopics in Important Dimensions of Complete Physics
2-Column TableRapid Revision — Important Dimensions of Complete Physics
Concept → Trap → Example1) Heat and Thermodynamics Dimensions
Dimensional Reference — Thermal QuantitiesHeat [ML²T⁻²], Specific heat [M⁰L²T⁻²θ⁻¹], Boltzmann constant [M¹L²T⁻²θ⁻¹], Stefan’s constant [M¹L⁰T⁻³θ⁻⁴], Planck’s constant [M¹L²T⁻¹].
- Specific heat and Boltzmann constant have identical dimensions [M¹L²T⁻²θ⁻¹] because both represent energy per unit temperature — the difference is per kg (specific heat) vs per molecule (Boltzmann). NEET uses this pair as distractors.
- Latent heat [M⁰L²T⁻²] has the same dimension as (velocity)² or gravitational potential — NEET may present these as ‘which quantity has the same dimension as latent heat’.
- Common NEET trap: confusing the dimensions of thermal conductivity [M¹L¹T⁻³θ⁻¹] with those of Stefan’s constant [M¹L⁰T⁻³θ⁻⁴]. The L exponent and θ exponent are different — check both.
2) Electricity Dimensions
Dimensional Reference — Electromagnetic QuantitiesCharge [M⁰L⁰T¹A¹], Capacitance [M⁻¹L⁻²T⁴A²], Resistance [M¹L²T⁻³A⁻²], Magnetic flux [M¹L²T⁻²A⁻¹], Permeability μ₀ [M¹L¹T⁻²A⁻²].
- Capacitance [M⁻¹L⁻²T⁴A²] and permittivity ε₀ [M⁻¹L⁻³T⁴A²] differ only in the L exponent (−2 vs −3). NEET exploits this by placing both in the same match-the-column question.
- The product RC has dimension of time: [M¹L²T⁻³A⁻²]×[M⁻¹L⁻²T⁴A²] = [T]. This is tested as ‘which combination has the dimension of time’ where RC competes with L/R.
- Common NEET trap: writing charge as [AT] but forgetting that the T exponent is +1, not 0. Since q = It, the dimension is [M⁰L⁰T¹A¹], and any option with T⁰ for charge is wrong.
US Curriculum Gaps — Important Dimensions of Complete Physics
NRI students from US high schools may find these specific gaps when preparing for NEET Physics dimensional formulae.Dimensional Formulae of Thermal Quantities (absent in AP Physics 1 / AP Physics 2)
US AP Physics courses present heat, specific heat, and Boltzmann constant with their SI units but never require students to express them in dimensional form [M^a L^b T^c θ^d]. NEET expects instant recall of these dimensions and uses them in direct MCQs.
- AP Physics 1 does not cover thermodynamics at all; AP Physics 2 covers it conceptually but without dimensional analysis.
- NEET requires students to derive [M¹L⁰T⁻³θ⁻⁴] for Stefan’s constant from its defining equation in under 60 seconds.
- Practice expressing every thermal quantity via its base equation (e.g., c = Q/(mΔT)) and substituting known dimensions.
Dimensional Formulae of Electromagnetic Quantities (limited in AP Physics C: E&M)
AP Physics C uses ε₀ and μ₀ in Coulomb’s law and Ampère’s law but does not require their dimensional expressions. NEET asks students to recall [M⁻¹L⁻³T⁴A²] for ε₀ and [M¹L¹T⁻²A⁻²] for μ₀ from memory and to verify c = 1/√(μ₀ε₀) dimensionally.
- AP Physics C derives electric field from Gauss’s law but never decomposes ε₀ into M, L, T, A exponents.
- NEET may ask ‘which of the following has the dimension [M¹L¹T⁻²A⁻²]?’ — US-trained students are unfamiliar with this format entirely.
- Build a conversion table: start from F = (1/4πε₀)(q₁q₂/r²), isolate ε₀, and substitute [F] = [MLT⁻²], [q] = [AT], [r] = [L].
NEET-Style Practice Questions — Important Dimensions of Complete Physics
4 NEET-style practice questionsPractice Problems — Important Dimensions of Complete Physics
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Physics — Important Dimensions of Complete Physics Revision Checklist
Use this section for quick chapter tracking before mocks, part tests, and final NEET revision.
Frequently Asked Questions — Important Dimensions of Complete Physics
Notes · Downloads · Revision · Important QuestionsWhy does NEET specifically test dimensional formulae of Planck’s constant and Stefan’s constant?
How do I distinguish between Boltzmann constant and specific heat capacity dimensionally?
What is the fastest way to derive the dimension of permittivity ε₀?
How do I remember whether capacitance has M⁻¹ or M¹?
Is the dimension of magnetic flux the same as that of inductance?
Why does latent heat have the same dimensions as the square of velocity?
How can I verify that the speed of light c satisfies c = 1/√(μ₀ε₀) dimensionally?
What is the dimensional formula of magnetic induction B, and how does it differ from magnetic flux?
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