Question

The internal resistance of a cell depends on the:
(A) Surface area of its electrodes
(B) Separation between its electrodes
(C) Nature, concentration and temperature of its electrolyte
(D) All of the above

Answer 1

Hint: To answer this question, we need to see the basic construction of a cell. Then, we will have to use the formula for the resistance of a conductor in terms of its length, area and resistivity from where we can find the correct option.

Formula used:
The formulae which are used in solving this question are given by
$R = \rho \dfrac{l}{A} $ , here $ R $ is the resistance, $ \rho $ is the resistivity, $ l $ is the length, and $ A $ is the area of a conductor.
$ \rho = \dfrac{1}{\kappa } $ , here $ \rho $ is the resistivity and $ \kappa $ is the conductivity.

Complete step by step solution:
A cell is basically an electrochemical setup of two electrodes dissolved in an electrolyte. Here, a chemical reaction takes place within the electrolyte, from which chemical energy is released which is utilised as the electrical energy of the cell. So, a current flows between the two electrodes, the anode and the cathode, through the electrolyte. When the current flows through this passage, it experiences a resistance to its flow, which is called the internal resistance of the cell. The whole passage of the current from the electrodes to the electrolyte can be equivalently assumed to be a conductor, whose length is equal to the separation between the electrodes, and whose cross sectional area is equal to the surface area of the electrodes. We know that the resistance in terms of the above parameters is given by
 $\Rightarrow R = \rho \dfrac{l}{A} $ ... (1)
Now, the resistivity of this resistance is linked with the conductivity of the electrolyte. We know that the resistivity is equal to the inverse of the conductivity, that is
 $\Rightarrow \rho = \dfrac{1}{\kappa } $
Writing (1) in terms of the parameters of the cell, we get the internal resistance of the cell as
 $\Rightarrow r = \dfrac{d}{{A\kappa }} $
So, as we can see that the internal resistance is directly proportional to the separation between the electrodes, and inversely proportional to the surface area of the electrodes.
Thus the options A and B are correct.
Also, the internal resistance is inversely proportional to the conductivity of the electrolyte. Now, the conductivity is different for different electrolytes. So it depends on the nature of the electrolyte.
Also, the conductivity for a given electrolyte is a function of its concentration. And lastly, it increases with the increase in temperature of the electrolyte.
So, the option C is also correct.
Hence, the correct answer is option D.

Note:
We should not be confused by the fact that the electrolyte is a liquid, while the formula for the resistance which we have used here is generally used for the solid conductors. We must note that this formula is not defined for a particular state of a conductor. It simply relates the dimensions of the conductor with its resistance. So, it can be applied in the case of a liquid conductor, the electrolyte too.