The correct answer is: A. at the head of water course.
The duty of a canal is the amount of land that can be irrigated by a given amount of water. The duty is largest at the head of the canal because the water is flowing at its highest velocity there. As the water flows down the canal, it loses some of its velocity and therefore some of its ability to irrigate land.
Option B is incorrect because the duty is not largest on the field. The duty is largest at the head of the canal, and it decreases as the water flows down the canal.
Option C is incorrect because the duty is not largest at the head of a main canal. The duty is largest at the head of the canal, and it decreases as the water flows down the canal.
Option D is incorrect because the duty is not the same at all places. The duty is largest at the head of the canal, and it decreases as the water flows down the canal.