Question

How is electrical conductance of a conductor related to the length and area of the cross section of the conductor?
(A) G = l.a.${{\text{k}}^{{{-1}}}}$
(B) G = k.l.${{\text{a}}^{{{-1}}}}$
(C) G = k.a.${{\text{l}}^{{{-1}}}}$
(D) G = k.${{\text{l}}^{{{-1}}}}$.${{\text{a}}^{{{-1}}}}$

Answer 1

Hint: Conductance is simply the reciprocal of resistance. It is defined as the ratio of current to voltage. It is expressed in siemens or mho.

Complete step by step answer: The resistance of a material is defined as the tendency of a material to stop the flow of current. It is denoted as R and measured in ohm.
We know that
\[{{R = \rho }}{\text{x }}\dfrac{{\text{l}}}{{\text{a}}}\]
where ρ is resistivity and l is the length of the wire in cm and a is the cross section area of wire in ${\text{c}}{{\text{m}}^{\text{2}}}$.
Conductivity is the reciprocal of resistivity(ρ). It is denoted as k.
\[{\text{k = }}\dfrac{{\text{1}}}{{{\rho }}}\]
Conductance is simply the inverse of resistance. It is denoted as G and measured in mho.
\[{\text{G = }}\dfrac{{\text{1}}}{{\text{R}}}\]
\[
   \Rightarrow {\text{G = }}\dfrac{{\text{1}}}{{\text{R}}}{\text{ = }}\dfrac{{\text{1}}}{{{{\rho }}{\text{x }}\dfrac{{\text{l}}}{{\text{a}}}}}{\text{ = }}\dfrac{{\text{k}}}{{\dfrac{{\text{l}}}{{\text{a}}}}}{\text{ [}}\because {\text{k = }}\dfrac{{{1}}}{{{\rho }}}{\text{]}} \\
   \Rightarrow {\text{G = k}}{\text{.a}}{\text{.}}{{\text{l}}^{{\text{ - 1}}}} \\
\]

So, the correct option is C.

Additional information: The electrical conductance of a conductor depends upon the length and area of the cross section of the conductor and also the conductivity. Conductance is the number which defines how much a material can assist the flow of current. Conductance is the reciprocal of resistance. It is mathematically expressed as ratio of current to voltage from Ohm’s law and it is measured in siemens or mho (i.e. ohm spelled backwards).

Note: Resistivity and conductivity are two different entities that are inversely related. So, the conductance depends upon the conductivity, k and not on the resistivity, ρ. Conductivity represents the amount of current flow thus high conductance means material has high ability to conduct current. In case of resistivity, the value must be low so that it means the material has high ability to readily flow current with less resistance. Thus, both the terms are inversely related to conductance in this way.