Question

The conductance can't be expressed in
A. ${\text{ mho}}$
B. ${\text{ (ohm}}{{\text{)}}^{ - 1}}$
C. ${\text{ Siemen}}$
D. ${\text{ ohm }}{{\text{m}}^{ - 1}}$

Answer 1

in order to solve the question, we have to examine each of the unit given in the question mho, ${{\text{(ohm)}}^{ - 1}}$ , Siemen, ${\text{ohm }}{{\text{m}}^{ - 1}}$and have to find whether conductance can be expressed in units along with this we will also use the knowledge about resistance to ensure the relations

Formula used:
$K \propto \dfrac{1}{R}$
Where, $K$ is referred to the conductance and $R$ is referred to the resistance.

Complete step by step answer:
Conductance refers to the ease by which the electric current is passed through a wire where as resistance refers to the opposes the current passes through the wire therefore after deducing the definition of resistance and conductance, we can say that they both are opposite of each other hence we could also say that conductance is indirectly proportional to resistance which gives us the relation,
$K \propto \dfrac{1}{R}$
Resistance has international standard unit (SI unit) = ohm

By seeing the relation, we can say that conductance has the unit ${{\text{(ohm)}}^{ - 1}}$. mho is also the unit by which we measure conductance it is the opposite of ohm it was suggested by the scientist Sir William Thomson (Lord Kelvin) in 1883 from then we also use mho.

In the 14th General Conference on Weights and Measures it was approved that siemens as a derived unit in 1971 after the scientist named Ernst Werner von Siemens whereas ${\text{ohm }}{{\text{m}}^{ - 1}}$is the unit in which we cannot express conductance.

Hence, the correct option is D.

Note: Many of the students will may confuse that either Siemen or mho which is the standard international unit (SI unit ) of conductance but in the 14th General Conference on Weights and Measures both mho and Siemens were recognised as the standard international unit (SI unit ).