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Work Function

In the follow...

Question

In the following $I$ refers to current and other symbols have their usual meaning. Choose the option that corresponds to the dimensions of electrical conductivity:

A

M L^{- 3} T^{- 3} I^{2}

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B

M^{- 1} L^{- 3} T^{3} I^{2}

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C

M^{- 1} L^{3} T^{3} I

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D

M^{- 1} L^{- 3} T^{3} I

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Solution

The correct option is B $M^{- 1} L^{- 3} T^{3} I^{2}$
Conductivity has relation, $σ = \frac{l}{A R} = \frac{l I}{A V}$ .

V has dimension $[M L^{2} T^{- 3} I^{- 1}]$ . Hence dimension of $σ$ is $[M^{- 1} L^{- 3} T^{3} I^{2}]$ .

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m

=

l

=

t

=

i

=

current. The dimensions of

\frac{{m l}^{2}}{t^{3} i}

are the same as that of:

ϵ_{0}

denote the permittivity of the vacuum and

μ_{o}

is permeability of vacuum.
If M

=

=

=

=

electric current, then
a)

ϵ_{0} = M^{- 1} L^{- 3} T^{2} I

ϵ_{0} = M^{- 1} L^{- 3} T^{4} I^{2}

μ_{0} = {M L T}^{- 2} I^{- 2}

ϵ_{0} = {M L}^{2} T^{- 1} I

Q. The physical quantity having the dimensions

[M^{- 1} L^{- 3} T^{3} A^{2}]

Q. Match the following two columns:

Column I	Column II
(a) Electrical resistance	(p) $M L^{3} T^{- 3} A^{- 2}$
(b) Electrical potential	(q) $M L^{2} T^{- 3} A^{- 2}$
(c) Specific resistance	(r) $M L^{2} T^{- 3} A^{- 1}$
(d) Specific conductance	(s) None of these

Q. The dimensional formula

M^{- 1} L^{3} T^{- 2}

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