Question

The unit of conductance is _____________ and that of specific conductance is ____________?
(a)-\[oh{{m}^{-1}};oh{{m}^{-1}}c{{m}^{2}}\]
(b)-\[oh{{m}^{-1}}c{{m}^{2}};oh{{m}^{-1}}c{{m}^{-1}}\]
(c)-\[oh{{m}^{-1}}c{{m}^{-1}};oh{{m}^{-1}}c{{m}^{2}}\]
(d)-\[oh{{m}^{-1}};oh{{m}^{-1}}c{{m}^{-1}}\]

Answer 1

Hint: For calculating the conductance, the concept of electrical resistance should be used. For calculating the specific conductance, the concept of specific resistance or resistivity should be used.

Complete answer:
Let us first understand what is conductance and how it can be calculated:
The reciprocal of the electrical resistance is called the conductance. It is usually represented by G.
Thus,
$G=\dfrac{1}{R}$
Now, what is electrical resistance?
The restriction in the flow of current is called electrical resistance. It is given by:
 $R=\dfrac{E}{I}$
Units of resistance:
$Ohms=\dfrac{Volts}{Amperes}$
Hence, resistance is in ohms.
It is observed that the resistance R of a conductor is directly proportional to its length and inversely proportional to its area of the cross-section is 1$c{{m}^{2}}$ :
\[R\propto \dfrac{l}{a}\]
$R=\rho \dfrac{l}{a}$
Where $\rho $is a constant of proportionality, called Specific resistance or resistivity.
Resistivity is defined as the resistance of a conductor whose length is 1 cm and the area of the cross-section is 1 .
The reciprocal of specific resistance is called specific conductance. It is denoted by $\kappa $ (kappa)
\[\kappa =\dfrac{1}{\rho }\]
The unit of specific resistance is ohm-cm.
So, the unit of specific conductance will be:$oh{{m}^{-1}}c{{m}^{-1}}$
Hence, the correct option is: (d)-$oh{{m}^{-1}};oh{{m}^{-1}}c{{m}^{-1}}$
So, the correct answer is “Option D”.

Note:Don't get confused between resistance and conductance because the formula and definition are similar, only reciprocal is the difference. The formula should be taken care of. Always take the units in the same dimension. And take the area in $c{{m}^{2}}$.