Question 166: Units , Dimensions and Error Analysis

Question

The quantities x = $${1 \over {\sqrt {{\mu _0}{\varepsilon _0}} }}$$, y = $${E \over B}$$ and z = $${l \over {CR}}$$ 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 :

Accepted Answer

x = $${1 \over {\sqrt {{\mu _0}{\varepsilon _0}} }}$$ = speed
$$ 	herefore $$ [x] = [L
1
T
Ã¢ÂÂ1
]
y = $${E \over B}$$ = speed
$$ 	herefore $$ [y] = [L
1
T
Ã¢ÂÂ1
]
z = $${l \over {CR}}$$ = $${l \over 	au }$$
$$ \Rightarrow $$ [z] = [L
1
T
Ã¢ÂÂ1
]
So, x, y, z all have the same dimensions.

Answer

Only y and z have the same dimension

Answer

x, y and z have the same dimension

Answer

Only x and y have the same dimension

Answer

Only x and z have the same dimension

Units , Dimensions and Error Analysis

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

Choose the correct answer: