First slide

Dimensions of physical quantities

Question

The quantities $x = \frac{1}{\sqrt{μ_{0} \in_{0}}}, y = \frac{E}{B}$ and $z = \frac{l}{C R}$ are defined where C-capacitance, R-Resistance, $l$ -length, E-Electric field, B-magnetic field and $\in_{0}, μ_{0} -$ free space permittivity and permeability respectively. Then :

Difficult

A

Only x and z have the same dimension
B

Only x and y have the same dimension
C

Only y and z have the same dimension
D

x,y and z have the same dimension

Solution

$\begin{array}{l} x = \frac{1}{\sqrt{μ_{0} ε_{0}}} \\ \Rightarrow d i m e n s i o n a l f o r m u l a o f x = [M^{0} L^{1} T^{- 1}] \\ y = \frac{E}{B} \\ \Rightarrow [y] = [M^{0} L^{1} T^{- 1}], \\ [z] = \frac{[L]}{[T]} = [L^{1} T^{- 1}] \end{array}$
So all quantities have same dimensional formula of velocity or speed.

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