Question

How is the electrical conductance of a conductor related with length and area of the cross section of the conductor?
(A) $G = l.a.{k^{ - 1}}$
(B) $G = k.l.{a^{ - 1}}$
(C) $G = k.a.{l^{ - 1}}$
(D) $G = k.l.{a^{ - 2}}$

Answer 1

Hint: Conductance is the ability of a conductor or solution to conduct charge or electricity through it while on the other hand resistance is the ability of any substance or solution to resist the flow of current through it.
  Complete answer:
-First of all let us understand what conductance is. The ease with which electric current flows through a conductor or the ability of the conductor to conduct electricity is known as electrical conductance (G).
The SI unit of conductance is Siemens (S) or mho (${\Omega ^{ - 1}}$).
-Now let’s talk about resistance. The electrical potential difference divided by the amount of current passing through the conducting solution is known as electrical resistance (R).
It is basically resistance to the flow of charge or electricity.
For a conductor with cross sectional area ‘a’ and length ‘l’, having resistivity ‘$\rho $’, resistance is written as:
                                                        $R = \rho l/a$ (1)

The SI unit of resistance is ohm, which is denoted by:$\Omega $
-From the above discussion we can see that conductance is the opposite of resistance.
So, we can say that conductance is the reciprocal of resistance. It can be written as:

                                                         $G = 1/R$ (2)
 And conductivity, $k = 1/\rho $ or $\rho = 1/k$ (3)

 In equation (2) put the value of R from (1). We get:
                                                       $G = a/\rho l$
In the above equation put the value of $\rho $ from equation (3). Now we get:
                                $G = k.a/l$ or $G = k.a.{l^{ - 1}}$

So, the correct option is: (C)$G = k.a.{l^{ - 1}}$

Note: Conductance (G) and resistance (R) should not be confused with each other since both are totally opposite things. Although the words speak for themselves but still remember that resistance is opposition to current flow while conductance is the ease with which current flows.