Final answer:
The question asks to calculate the internal resistance of a cell using the change in terminal potential difference when a circuit is closed. The formula applies, and knowledge of the external resistance R allows calculation of the internal resistance.
Step-by-step explanation:
The question deals with the concept of internal resistance in electrical circuits, specifically in relation to the effect of a voltage source like a cell. The terminal potential difference (PD) of a cell changes depending on whether the circuit is open or closed, which allows one to calculate the internal resistance of the cell. The technical question requires an application of the formula V = emf - Ir, where V is the terminal voltage, emf is the electromotive force, I is the current, and r is the internal resistance.
When the key is closed, the current flows and some of the voltage is lost across the internal resistance, hence the PD across the terminals drops from 6 volts to 4 volts. The loss in PD (2 volts) when the key is closed is due to the internal resistance of the cell. The current flowing in the circuit can be found if the external resistance R is known, and from there, the internal resistance r can be calculated using the equation.