Question

SI unit of conductivity is ---------
a.) ${Sm }^{ -1 }$
b.) ${ Ss }^{ -1 }$
c.) ${ Sm }^{ 1 }$
d.) None of these

Answer 1

Hint : For solving this question we have to know about conductivity i.e. conductivity of any substance is the ability to allow electricity through ions. It can be of ionic, thermal or electrical. This unit measures the current flow through an electrolyte.

Complete step by step solution :
First of all, it is necessary to know the specific resistance (resistivity).
Resistivity or specific resistance of a material is a measure of the resistance, which it provides to the flow of current through it: specific resistance depends upon composition, temperature, pressure of the material. The reciprocal of resistivity is defined as specific conductance which is the ability to conduct electricity
When electric current is passed through metallic rod of same cross-section then resistance of rod (R) is directly proportional to length of rod (L) and inversely proportional to the area of cross-section (A) of it.
$R\alpha \cfrac { L}{ A }\\\ R=\rho \cfrac { L }{ A }$
Here, $\rho$ is a constant which is called specific resistance of conductor.
This constant has different values for different materials as we know specific resistance is dependent on the physical properties of Material like density and composition. For unit length and unit cross-sectional area, i.e. L=1cm and $A={ 1cm }^{ 2 }$
$\rho =R$
This condition can be useful for understanding resistivity.
Now let’s learn resistivity in terms of this condition, so the resistance of a homogenous chunk of a substance of unit length and unit cross-section is defined as the resistivity or specific resistance of the substance. Numerically,
$\rho =\dfrac { RA }{ L } \\\ \sigma =\dfrac { 1 }{ \rho }$
Specific resistivity is reciprocal to specific conductance which is denoted by $\sigma$.
From the Specific resistance formula,
$\rho =\dfrac{unit\quad of\quad R\times unit\quad of\quad A}{unit\quad of\quad L}$
When resistance R is expressed in ohm ($\Omega$), area (A) and length (L) are expressed in ${ cm }^{ 2 }$ and centimeters (cm) respectively. Then, the unit of resistivity is $\Omega$.cm. If the area and length are expressed in ${ m }^{ 2 }$ and metre (m) respectively, the SI unit of resistivity is $\Omega$.m.
Unit of specific conductance can be determined, as we know conductivity is the reciprocal of resistivity so,
$\sigma ={ ohm }^{ -1 }\times \cfrac { cm }{ { cm }^{ 2 } }$
Unit of conductivity is ${ ohm }^{ -1 }{ m }^{ -1 }$ or siemens ${ m }^{ -1 }$
So, the correct answer is “Option A”.

Note : IUPAC recommended resistivity term to specific resistance. Similarly, specific conductance is referred to its conductivity. So, the conductance of 1ml solution is called specific conductance.
”Conductance and conductivity are measured by determining the resistance and resistivity of electrolytic solution through a wheatstone bridge filled in specific types of conductivity cells.”