Question

Multiple Correct Answers Type
Consider the quantities : $x=\frac{E}{b},y=\frac{1}{{\mu }_0{ϵ}_0}$, and $z=\frac{l}{CR}$.
Here , l is the length of a wire, C is the capacitance, and R is a resistance. All other symbols have usual meanings. Then

• A. x and y have the same dimensions.
• B. x and z have the same dimensions.
• C. y and z have the same dimensions.
• D. None of the above three pairs have the same dimensions.

Answer 1

Answer: (A), (B), (C)

The correct options are
A x and y have the same dimensions.
B x and z have the same dimensions.
C y and z have the same dimensions.

$\left[E\right]=\left[{ML}^3{T}^{-3}\right]$

$\left[B\right]=\left[{MTA}^{-1}\right]$

$C=\frac{1}{\sqrt{{\epsilon }_0{\mu }_0}}$ [where $C$ is the speed of light]

$Y=C^2=\left[M^2{T}^{-4}\right]$

$\left[capacitance\right]=\left[M^{-1}{L}^{-2}{T}^4{A}^2\right]$

$\left[R\right]=\left[{ML}^2{T}^3{A}^{-2}\right]$