Я по ошибке выключил свет.

Because this is the past tense masculine singular form of выключить.

In Russian, past tense verbs agree with the subject in gender and number:

• я выключил = I turned off / I switched off (male speaker)
• я выключила = I turned off / I switched off (female speaker)
• мы выключили = we turned off

So if the speaker is a man, выключил is correct. If the speaker is a woman, it would be Я по ошибке выключила свет.

Выключил is perfective, while выключал is imperfective.

Here, the sentence describes one completed action: the light ended up off. That is why Russian uses the perfective verb:

• выключил = turned off, completed the action

If you used выключал, it would usually sound like:

• a repeated action,
• a process,
• or background information rather than a single completed result.

For example:

• Я выключал свет каждый вечер. = I used to turn off the light every evening.

So in this sentence, выключил is the natural choice.

По ошибке is a fixed expression meaning by mistake.

Grammatically, it uses:

• по
  • dative case
• ошибка becomes ошибке

So:

• ошибка = mistake, error
• по ошибке = by mistake

It functions like an adverbial phrase, explaining how or under what circumstances the action happened.

Very common examples:

• Я по ошибке взял не тот телефон. = I took the wrong phone by mistake.
• Она по ошибке отправила письмо не тому человеку. = She sent the letter to the wrong person by mistake.

Yes, very often you can.

• Я по ошибке выключил свет.
• Я случайно выключил свет.

Both can mean I turned off the light by mistake / accidentally.

But there is a slight nuance:

• случайно = accidentally, unintentionally
• по ошибке = by mistake, because of an error

So по ошибке emphasizes the idea of a mistake, while случайно emphasizes that it was not intentional. In many everyday situations, though, they overlap.

Свет is in the accusative case because it is the direct object of выключил.

You are turning off what?

• свет

For inanimate masculine nouns, the accusative singular looks the same as the nominative singular:

• nominative: свет
• accusative: свет

So the form does not change, even though the case does.

Yes, Russian often omits subject pronouns when they are clear from the verb form or context.

So you can say:

• По ошибке выключил свет.

That can still mean I turned off the light by mistake, especially in conversation.

But Я may be included:

• for clarity,
• for emphasis,
• or simply because the speaker chooses to state it explicitly.

So both are possible:

• Я по ошибке выключил свет.
• По ошибке выключил свет.

The version with Я is a little more explicit.

Yes. Russian word order is flexible, and changing it changes the focus or emphasis, not usually the basic meaning.

Possible versions:

• Я по ошибке выключил свет.
  Neutral: I turned off the light by mistake.

• По ошибке я выключил свет.
  Slightly emphasizes by mistake.

• Свет я выключил по ошибке.
  Emphasizes the light specifically.

Russian uses word order much more for emphasis than English does, because case endings already show grammatical roles.

For lights, выключить свет is the standard expression and means to turn off the light(s).

Related verbs exist, but they are not always interchangeable:

• выключить свет = turn off the light
• включить свет = turn on the light

Compare with:

• отключить электричество = disconnect the electricity / cut off power
• погасить свет = switch off the light / extinguish the light, also possible but with a different feel

So for normal everyday speech about switching a light off at a switch, выключить свет is the most standard choice.

In Russian, свет here is a very common mass-style noun meaning the light in the room or space.

Russian has no articles, so свет can correspond to:

• the light
• sometimes lights, depending on context

In this sentence, the natural interpretation is simply that the speaker switched off the lighting.

So even though English often says the light, Russian just says свет.

A woman would say:

• Я по ошибке выключила свет.

The only change is the past tense verb ending:

• male speaker: выключил
• female speaker: выключила

Everything else stays the same.

Russian past tense often covers both ideas that English separates into:

• I turned off the light by mistake
• I have turned off the light by mistake

The form выключил is simply the Russian past tense. Whether English uses simple past or present perfect depends on context and style.

So Russian does not need a separate form here.

The main stresses are:

• Я
• по оши́бке
• вы́ключил
• свет

Especially useful ones to remember:

• оши́бка
• по оши́бке
• вы́ключить
• вы́ключил

Stress is important in Russian, because it is not always predictable and can affect pronunciation a lot.