Is there a one-to-one relationship between active and passive voice in English, and what are reasons for using the passive rather than the active?
I will try to answer this question by helping you understand the difference between active and passive voice.
In a typical sentence there is a subject and a verb. In an active (voice) sentence, the subject performs the action:
Amy kicked the ball. - or - Amy kicks the ball. (Amy is the subject, kick is the verb and ball is a direct object.)
In a passive (voice) sentence, the subject is acted upon (passive, behind the scenes) rather than the performer of the action:
The ball was kicked by Amy. (Ball is now the subject, was kicked is the verb phrase, and Amy has become the object of the preposition.)
In general, writing guides (like Zinsser's On Writing Well) tell us to avoid passive voice as much as possible. They say this because it is slow, muddy, wordy, and well, passive. Passive sentences take no command. They sit in the background. They are kind.
Those then, I suppose would be reasons for using passive voice. If you are attempting a polite or submissive tone - or if you simply want to sound uncommanding (almost like you don't wish to step on any toes) you might use passive voice.
Passive voice also takes the emphasis (in the above sentence) off of Amy and puts it on the ball. Using the same example, the passive voice might be necessary if you had several objects (a ball, a balloon and a bunny for example.) If you wanted the focus on the objects instead of the people doing things to them, you'd use passive voice. The ball was kicked by Amy. The balloon was kicked by Fred. The bunny was kicked by Billy.
Obviously consider this a simple metaphor that could be applied to a different piece of writing.