Correct Option: (B)

Step 1 (Governing Principles & Definitions): [1 Mark]

• The terminal potential difference $V$ of a cell during discharge is given by the relation: $$V = \varepsilon - Ir$$ where $\varepsilon$ is the emf, $I$ is the current, and $r$ is the internal resistance.
• The internal resistance $r$ of a cell arises due to the opposition offered by the electrolyte to the flow of ions. As temperature decreases, the viscosity of the electrolyte increases, hindering ion mobility.

Step 2 (Analysis of Statements): [2 Marks]

• Statement (A) & (C): During discharge, the cell acts as a source. The potential drop across internal resistance is $Ir$, thus $V = \varepsilon - Ir$. Since $Ir > 0$, $V < \varepsilon$. These are correct.
• Statement (D): Rearranging $V = \varepsilon - Ir$ into the linear form $y = mx + c$: $$V = (-r)I + \varepsilon$$ This represents a straight line with a negative slope ($-r$) and a y-intercept ($\varepsilon$). This is correct.
• Statement (B): The internal resistance $r$ is inversely proportional to the mobility of ions. When the temperature of the electrolyte decreases, the viscosity increases, which reduces the mobility of ions. Consequently, the internal resistance $r$ increases, not decreases. Therefore, this statement is incorrect.

Step 3 (Final Conclusion): [1 Mark]

Since statement (B) contradicts the physical behavior of electrolytes where lower temperatures lead to higher viscosity and higher internal resistance, it is the incorrect statement.

💡 EL10 Concept Insight: Think of the electrolyte like honey; when it gets cold, it becomes thick and sticky, making it much harder for the "charge-carrying" ions to swim through it, which is why the internal resistance actually goes up when it's cold!