Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
Highly selective Backlog Qs for JEE MainPhysicsUnits and Dimensions

The expressions below give current I through an electronic component as a function of applied potential V . I₀ and V₀ are constants having dimensions of current and potential respectively. Which of the following are dimensionally incorrect? (A) I=I₀ (e^ 2 V V₀ +1 ) (B) I=I₀ (e^ v 2 V₀ -1 ) (C) I=I₀ V₀ (e^ V V₀ -1 ) (D) I=I₀ ( V V₀ ) (e^ V V₀ -1 )

Options

  1. AA
  2. BB
  3. CC
  4. DD

Correct answer

C. C

Step-by-step solution

According to the principle of homogeneity, a physical equation will be dimensionally correct only if the dimensions of all the terms occuring on both side of the equation are the same. Hence, in option (c) I=I₀ V₀ (e^ v V₀ -1 ) Dimension of I dimensions of I₀ V₀ Therefore, equation shown in option (c) is not dimensionally correct.

Practice Units and Dimensions on Quantrex Academy →

More from Units and Dimensions

In a new system of units, the units of mass, length, time and current are 5 kg, 5 m, 5 s and 5 A, respectively. If ₀ and ₀ are the permeability and permittivity of free space, resp 2026A new unit ( ) of length is chosen such that it is equal to the speed of light in vacuum. What is the distance between Venus and Earth in terms of units if light takes 6 min. 40 s 2026Consider the equation H = x^p ^q E^r t^s , where H= magnetic field; E= electric field, = permittivity, x= distance, t= time. The values of p, q, r and s respectively are: 2026The percentage error in the calculated volume of a sphere, if there is 2 % error in its diameter measurement, is __________. 2026Match List - I with List - II. List - I List - II A. Boltzmann constant I. [M⁻¹L^3T⁻²] B. Stefan's constant II. [ML^2T⁻¹] C. Planck's constant III. [ML^2T⁻²K⁻¹] D. Gravitational co 2026The potential energy of a particle changes with distance x from a fixed origin as V = A x x + B , where A and B are constant with appropriate dimensions. The dimensions of AB are _ 2026Match List-I with List-II. List-I List-II A. Meter (L) I. hc G B. Second (S) II. Gh c^5 C. Kilogram (M) III. K^2L^2c^3 Gh D. Kelvin (K) IV. Gh c^3 where h (Planck's constant), G (g 2026L , C and R represents physical quantities inductance, capacitance and resistance respectively. The dimensional formula ML^2 T⁻⁴ A⁻² corresponds to __________. 2026 Full Units and Dimensions list All Highly selective Backlog Qs for JEE Main PYQs