Question

The quantities $x=\frac{1}{\sqrt{{\mu }_0{\epsilon }_0}},y=\frac{E}{B}$ and $z=\frac{l}{CR}$ are defined, where $C$-capacitance, $R$-Resistance, $l$-length, $E$-Electric field, $B$-magnetic field and ${\epsilon }_0,{\mu }_0$-free space permittivity and permeability respectively. Then

• A. $x,y$ and $z$ have the same dimension.
  
• B. Only $x$ and $z$ have the same dimension.
  
• C. Only $x$ and $y$ and have the same dimension.
  
• D. Only $y$ and $z$ and have the same dimension.

Answer 1

The correct option is A $x,y$ and $z$ have the same dimension.


We know that

Speed of light, $c=\frac{1}{\sqrt{{\mu }_0{\epsilon }_0}}=x$

Also Speed of light, $y=\frac{E}{B}=c$

Time constant, $\tau =RC=t$

$\therefore z=\frac{1}{Rc}=\frac{l}{t}=\text{Speed}$

hence $x,y,z$ have same dimensions