Question

Internal resistance of a battery cell increases with:
a.) Increase in the concentration of electrolyte
b.) Increase in the distance between electrodes
c.) Increase in area of the plates inside the electrolyte
d.) Increase in the size of electrodes

Answer 1

Hint: The inverse of conductance is resistance. Conductance is the degree to which an object conducts electricity, calculated as the ratio of the current which flows to the potential difference present.

Complete step-by-step answer:
We know that conductance is inversely proportional to the resistance of a specific material. The experimentally measured conductance, G, of a solution is that of a certain volume of the solution contained between the electrodes of the conductivity cell. The meter actually measures the resistance, R, of the solution between the electrodes and converts it to conductance.
\[G = \dfrac{1}{R}\]…. Eq. 1
To use this quantity to compare different solutions, a different quantity is introduced called specific conductivity, k
k = G Cell constant …. Eq. 2
Cell constant of any cell describes its geometry.
Cell constant = \[\dfrac{l}{A}\] …… Eq. 3
 where l is the distance between the electrodes and A is the area of the electrode.

Hence, combining equation 2 and 3, we get
K = \[\dfrac{{Gl}}{A}\]
Now, using equation 1, we get
K = \[\dfrac{l}{{AR}}\]
∴ R = \[\dfrac{l}{{Ak}}\]

Hence, the resistance of the battery cell is inversely proportional to the area of plates and is directly proportional to the distance between the electrodes. It is independent of the concentration of the solution.

Therefore, the correct answer is (B) Increase in the distance between electrodes.

Note: Do not confuse between conductivity and specific conductance. Specific conductance is the conductivity when the distance between the electrodes is 1cm and the electrodes have a unit area.