JEE Main201912 Apr 2019Morning ShiftPhysicsUnits and DimensionsActual
Which of the following combinations has the dimension of electrical resistance ( ϵ 0 is the permittivity of vacuum and μ 0 is the permeability of vacuum)?
Options
- Aϵ 0 μ 0
- Bϵ 0 μ 0
- Cμ 0 ϵ 0
- Dμ 0 ϵ 0
Correct answer
D. μ 0 ϵ 0
Step-by-step solution
Resistance = Volt Ampere = M L 2 T - 3 A - 1 A = M L 2 T - 3 A - 2 We know, μ 0 = M L T - 2 A - 2 ε 0 = M - 1 L - 3 T 4 A 2 Hence, μ 0 ε 0 = μ 0 ε 0 = M L T - 2 A - 2 M - 1 L - 3 T 4 A 2 1 / 2 = M 2 L 4 T - 6 A - 4 1 / 2 = M L 2 T - 3 A - 2