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)?

Options

A. `sqrt((epsilon_(0))/(mu_(0)))`
B. `sqrt((mu_(0))/(epsilon_(0)))`
C. `(mu_(0))/(epsilon_(0))`
D. `(epsilon_(0))/(mu_(0))`

Answer

B

Explanation

`V=IR, R=V/I, R=(w//q)/I, R=(Ml^(2)T^(-2))/(I^(2)r)`
`r=[ML^(2)T^(-3)A^(-2)], F=1/(4piepsilon_(0)) (q_(1)q_(2))/(r^(2)), epsilon=(q_(1)q_(2))/(F_(1)r^(2))`
`epsilon_(0)=(A^(2)T^(2))/(MLT^(-2)L^(2)), epsilon_(0)=(A^(2)T^(2))/(ML^(3)T^(-2)), epsilon_(0)=[M^(-1)L^(-3)T^(4)A^(2)], C^(2)=1/(mu_(0)epsilon_(0))`
`mu_(0)=1/(C^(2)epsilon_(0)), mu_(0)=1/(L^(2)T^(-2)M^(-1)L^(-3)T^(4)A^(2)), mu_(0)=(M^(1)A^(-2)LT^(-2)), (epsilon_(0))/(mu_(0))=(M^(-1)L^(-3)T^(4)A^(2))/(M^(1)A^(-2)LT_(2))`
`(epsilon_(0))/(mu_(0))=M^(-2)L^(-4)T^(6)A^(4), (mu_(0))/(epsilon_(0))=M^(2)L^(4)T^(-6)A^(-4), sqrt((mu_(0))/(epsilon_(0))=ML^(2)T^(-3)A^(-2)`