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Which of the following combinations has ...

Which of the following combinations has the dimension of electrical resistance (`in_(0)` is the permittivity of vacuum and `mu_(0)` is the permeability of vacuum)?

A

`mu_0/epsilon_0`

B

`sqrt(mu_0/epsilon_0)`

C

`epsilon_0/mu_0`

D

`sqrt(epsilon_0/mu_0)`

Text Solution

Verified by Experts

The correct Answer is:
B
`[epsilon_0]=[M^(-1)L^(-3)T^(4)A^2]`
`[mu_0]=[M^(1) L^2 T^(-2)A^(-2)]`
`[R] = [ML^(2) T^(-3) A^(-2)]`
`[R] =[epsilon_0]^(a)[mu_0]^(b)`
`[ML^(2)T^(-3)A^(-2)]=[M^(-a) L^(-3a)T^(4a) A^(2a)M^(b) L^(2b)T^(-2b) A^(-2b)]`
`2a -2b =-2`
`a - b =-1 " "...(i)`
`4a -2b =-3 " "...(ii)`
`2a - 2b =-2 " "...(iii)`
`2a =-1 `
`a = -1/2 , b =1/2 implies [R] =sqrt(mu_0/epsilon_0)`
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