# The quantities $x = \frac{1}{\sqrt{\mu_o\epsilon_o}}, y = \frac{E}{B}$ and $z = \frac{2}{CR}$  are defined where C - capacitance, R - resistance, l - length, E - Electric field, B - magnetic field $\epsilon_o \mu_o$ - free space permittivity and permeability respectively, then: Option: 1 only y and z have same dimension Option: 2 only x and z have same dimension Option: 3 only x and y have same dimension Option: 4 x, y, and z have same dimension

Correct Answer: 4) x, y, and z have same dimension

$x=\frac{1}{\sqrt{\mu_{0} \epsilon_{0}}}\\ \text{As we know, speed of light},\\ c=\frac{1}{\sqrt{\mu_{0} \epsilon_{0}}} \\ \therefore[c]=[x]=\left[L T^{-1}\right]$

\begin{aligned} y &=\frac{E}{B} \\ \text { And } & c \text { is also equal to } \frac{E}{B} \\ & \therefore[c]=[y]=\left[L T^{-1}\right] \end{aligned}

$z=\frac{l}{CR} \Rightarrow[z]=\frac{[L]}{[C][R]}=\frac{(L]}{\left[M^{-1} L^{-2} T^{4} A^{2}\right]\left[M L^{2-3} A^{-2}\right]}=[LT^{-1}]$

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