If one of a person's hands is, Heaven forbid, bandaged or in a cast, and cannot be washed, he washes the other hand upon waking in the morning, pouring water on it three times. Although he washes only one hand, he recites the usual text of the Beracha – "Al Netilat Yadayim," which speaks of washing "Yadayim" – "hands," in the plural form. He does not change the text of the Beracha to "Yad," despite the fact that he washes just one hand.
The Beracha over Netilat Yadayim differs in this respect from the Beracha recited over the Misva of immersing new utensils, whose text depends on the number of utensils being immersed. If one immerses two or more utensils, then he recites the Beracha "Al Tebilat Kelim," referring to the immersion of multiple utensils ("Kelim"), whereas one who immerses just a single utensil recites "Al Tebilat Keli," making reference to one utensil ("Keli").
Rav Yisrael Bitan explained that when the Sages instituted the Beracha over immersing utensils, they took into account the reality that people sometimes immerse just a single utensil, and other times immerse multiple utensils. Therefore, they formulated different texts for these two different situations. Netilat Yadayim, however, is almost always performed by washing both hands, and it is only in rare, unfortunate circumstances that a person washes just one hand. Therefore, the Sages formulated just a single text for the Beracha – "Al Netilat Yadayim," making reference to both hands, and this is the text that should be recited even if one washes only one hand.