Final answer:
The ratio of emf of two cells when connected in series and upon reversing the polarity of one cell indicates that the greater emf overcomes the lesser one. The two conditions provided by the potentiometer readings allow us to solve for the ratio, leading to a 3:1 ratio of emf between the two cells.
Step-by-step explanation:
The question involves understanding how the emf (electromotive force) of two cells changes when they are connected in series and when the polarity of one cell is reversed. When connected in series without reversing any cell, the cells balance at 6m on a potentiometer, which is directly proportional to their combined emf. When the polarity of one of the cells is reversed, they balance at 2m, indicating the effect of the cells opposing each other. This effect reduces the combined emf, which now equals the difference in emf between the two cells.
To find the ratio of emf of the two cells, we consider two equations based on the potentiometer reading: E1 + E2 is proportional to 6m (without reversing polarity), and E1 - E2 is proportional to 2m (with reversed polarity). Solving these two equations simultaneously gives us the ratio of the emfs. The ratio of E1 to E2 is 3:1, which is option A of the given choices.