The dimension of (μ_0)/( _0) is equal to that of : ( μ_0= Vacuum permeability and _0= Vacuum permittivity)

Correct answer: D. Resistance aligned & L=(μ_0 N A)/( ) & C=(A _0)/(d) & (L)/(C) (μ_0)/( _0) & (μ_0)/( _0) (L)/(C) & (L)/(C)=( R)/(( / R))=R^2 & (μ_0)/( _0) =R aligned

JEE Main 20257 AprilEvening Shift

Exam: JEE Main
Year: 2025
Date: 7 April
Shift: Evening Shift
Subject: Physics
Chapter: Units and Dimensions

JEE Main 2025 · 7 April · Evening Shift · Physics · Units and Dimensions

The dimension of (μ_0)/( _0) is equal to that of : ( μ_0= Vacuum...

The dimension of

\sqrt{\frac{\mu_0}{\epsilon_0}}

is equal to that of :
(

\mu_0=

Vacuum permeability and

\epsilon_0=

Vacuum permittivity)

Options

AVoltage
BCapacitance
CInductance
DResistance

Correct answer

D. Resistance

Step-by-step solution

\begin{aligned} & L=\frac{\mu_0 N A}{\ell} \\ & C=\frac{A \epsilon_0}{d} \\ & \frac{L}{C} \propto \frac{\mu_0}{\epsilon_0} \\ & \sqrt{\frac{\mu_0}{\epsilon_0}} \propto \sqrt{\frac{L}{C}} \\ & \frac{L}{C}=\frac{\tau R}{(\tau / R)}=R^2 \\ & \sqrt{\frac{\mu_0}{\epsilon_0}}=R\end{aligned}

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… JEE Advanced 2026 A new unit (α) of length is chosen such that it is equal to the speed of light in vacuum.… JEE Main 2026 Consider the equation H = (x^p ε^q E^r)/(t^s) , where H= magnetic field; E= electric… JEE Main 2026 The percentage error in the calculated volume of a sphere, if there is 2\% error in its… JEE Main 2026 Match List - I with List - II. List - I List - II A. Boltzmann constant I. [M^ -1 L^3T^… JEE Main 2026 The potential energy of a particle changes with distance x from a fixed origin as V = A x… JEE Main 2026 Match List-I with List-II. List-I List-II A. Meter (L) I. (hc)/(G) B. Second (S) II.… JEE Main 2026 L , C and R represents physical quantities inductance, capacitance and resistance… JEE Main 2026 Full Units and Dimensions list All JEE Main PYQs