Final answer:
The accuracy of a potentiometer is highest when the standard emfs and resistances are of the same order of magnitude, which allows for precise balancing and accurate measurements without current introducing significant errors. Option d is the correct answer.
Step-by-step explanation:
If a potentiometer is used to measure cell emfs on the order of a few volts, the most accurate measurements occur when the standard emfs are of the same order of magnitude and the resistances are in the range of a few ohms. The potentiometer is a null measurement device, which means it measures voltage by balancing an unknown emf against a known reference emf without drawing current from the unknown source.
This method relies on the principle that emf is directly proportional to the resistance in the segment of wire that is part of the potentiometer circuit. When the standard emf closely matches the unknown emf, the balance can be more precisely achieved, and the resistances being of a similar scale ensure that the current flowing through the circuit doesn't introduce significant errors. In contrast, large differences in magnitudes could lead to less precise balancing and inaccurate measurements.
Therefore, the correct option for why it is most accurate for standard emfs to be the same order of magnitude and resistances to be a few ohms is:
d) Potentiometers are most accurate when standard emfs and resistances are of the same order of magnitude.