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Question:

The quantities $x=\frac{1}{\sqrt{\mu_{0} \varepsilon_{0}}}, y=\frac{E}{B}$ and $z=\frac{1}{C R}$ are

defined where $C$-capacitance, $R$-Resistance, $l$-length, $E$-Electric field, $B$-magnetic field and $\varepsilon_{0}, \mu_{0}$, – free space permittivity and permeability respectively. Then :

1. $x, y$ and $z$ have the same dimension.

2. Only $x$ and $z$ have the same dimension.

3. Only $x$ and $y$ have the same dimension.

4. Only $y$ and $z$ have the same dimension.

Correct Option: 1

Solution:

(1) We know that

Speed of light, $c=\frac{1}{\sqrt{\mu_{0} \varepsilon_{0}}}=x$\

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

Time constant, $\tau=R c=t$

$\therefore z=\frac{l}{R c}=\frac{l}{t}=$ Speed

Thus, $x, y, z$ will have the same dimension of speed.