'Active' and 'Passive' in writing refer to neither tense nor tone, but to voice.
The active voice sentence order is subject-verb-objective (or complement). The passive voice order reverses this: object, a tense of the verb "to be" with the past participle of the sentence verb and then "by [the subject]." The subject can often be dropped.
Here's an example:
Active: The dog [subject] bit the boy [object].
Passive: The boy [object] was bitten by the dog [subject]. or The boy [object] was bitten.
In the use of 'objective' versus 'subjective' writing, you can use either voice to achieve either goal.
The objective/subjective connection comes in when people are writing reports in which the observer is expected to appear impartial because the passive voice allows you to drop the use of 'I' (or hide the 'I' or other actor).
Using the example above, you can use the passive voice to hide the culprit (dog) which can be useful at times :-). Alternatively, you can use it to suggest that the observation, not the observer, is the important information.
On the other hand, the active voice generally produces greater clarity, particularly in sentences with several modifying phrases and/or clauses.
I've consciously chosen to use 'you' in many of the sentences above, in order to avoid using the passive or using 'one' as the subject. ('One' can sound pretentious in American English, although perhaps not in other Englishes.)
In my opinion, the best discussion of these issues can be found in Williams' Style: Ten Lessons Pearson/Longman.
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