érzi zài chēguǎnsuǒ.

Here 在 is a main verb meaning to be at / to be in / to be located at.

So the pattern is:

Subject + 在 + Place

In this sentence:

• 儿子 = son
• 在 = is at
• 车管所 = the vehicle administration office / DMV

So 儿子在车管所 means The son is at the DMV or My son is at the vehicle administration office, depending on context.

Because Chinese usually uses 在, not 是, when talking about someone’s location.

• Correct: 儿子在车管所。
• Not natural: 儿子是车管所。

是 links one noun to another noun, like A is B:

• 他是老师。 = He is a teacher.

But for location, Chinese normally uses 在:

• 他在学校。 = He is at school.

So in this sentence, 在 is the right word because the sentence is about where the son is.

By itself, 儿子 literally means son. In real conversation, it can mean:

• my son
• the son
• his/her son

The exact meaning depends on context.

Chinese often leaves out possessive words like 我的 when they are already understood. So if you are talking about your family, 儿子在车管所 will very often be understood as My son is at the DMV.

If you want to be fully explicit, you can say:

• 我儿子在车管所。 = My son is at the DMV.
• 他的儿子在车管所。 = His son is at the DMV.

Yes. 儿子 is usually pronounced:

• érzi

The first syllable 儿 is second tone: ér
The second syllable 子 is usually a neutral tone here: zi

So it sounds like érzi, not érzǐ in normal speech.

Also, this 儿 is just the normal syllable ér meaning part of the word 儿子. It is not the same thing as erhua (the added -r sound you hear at the end of some northern words).

车管所 is short for 车辆管理所, which is an office that handles vehicle-related administration.

A natural English translation is often:

• the DMV
• the vehicle administration office
• the motor vehicle office

Character by character:

• 车 = vehicle / car
• 管 = manage / administer
• 所 = office / institute / place

So 车管所 is not just any car-related place; it specifically refers to the government office for vehicle registration, licensing, and similar matters.

Usually, no. 儿子在车管所 is already natural and complete.

You can also say:

• 儿子在车管所里。

That also means The son is in the DMV / at the vehicle administration office.

The version without 里 is very common and often more neutral. Adding 里 can make the sense of inside a little more explicit, but in many cases it is optional.

So:

• 在车管所 = at the DMV
• 在车管所里 = in the DMV / inside the DMV

Both are fine.

By itself, it usually just means he is there.

So 儿子在车管所 normally tells you his location, not his job.

If you want to say he works there, Chinese would often say something clearer, such as:

• 儿子在车管所工作。 = My son works at the DMV.
• 儿子是车管所的工作人员。 = My son is a staff member at the DMV.

Without extra words, the sentence mainly answers Where is he?

It is similar in meaning, but the structure is very direct in Chinese:

Subject + 在 + Place

Examples:

• 儿子在车管所。 = The son is at the DMV.
• 他在家。 = He is at home.
• 妈妈在学校。 = Mom is at school.

English uses is at/in, but Chinese simply uses 在 as the location verb.

So once you learn this pattern, many basic location sentences become easy to build.

In normal Chinese grammar, 在 is the verb here, so the sentence is complete.

From an English learner’s point of view, it may look like there is no separate word for is, but 在 is doing that job for location.

So Chinese is not missing a verb here. The verb is 在.

It is very common in everyday Chinese, and yes, it is also effectively a shortened form of 车辆管理所.

Native speakers regularly say 车管所 in normal conversation. You do not need to use the full form unless the situation is very formal.

So for learners, 车管所 is the practical word to remember.