The correct answer is: A. At culmination.
Polaris is the North Star, and it is always directly overhead at the North Pole. At any other latitude, Polaris will be located somewhere in the northern sky, but it will never be directly overhead. The altitude of Polaris in the sky will be equal to the latitude of the observer’s location.
Culmination is the highest point in the sky that a celestial object reaches during its daily apparent motion. Polaris culminates at midnight on the day of the winter solstice at the North Pole. At all other latitudes, Polaris culminates at a different time of day, depending on the observer’s latitude.
Elongation is the angular distance between a celestial object and the Sun. Polaris has an elongation of 90 degrees at the time of the winter solstice. At all other times of the year, Polaris has an elongation of less than 90 degrees.
Therefore, Polaris is usually observed for the determination of the latitude when it is at culmination.