How to take the minimum id from a particular SQL set?

Question

SQL

The Car table is the parent table. The Human table is a child table (the foreign key car_id of the Human table refers to the car_id of the Car table).
The Car table has 2 fields: car_id (int) and model (varchar). Model stores car brands. But these marks are repeated, ie. a car, for example Huinday, can have id 1 and 5. And two people from the Human table in the car_id field can have values ​​1 and 5. That is, these different people have the same car brand (Huinday), but their car_id is different.
I want this car_id to become single now and there is no confusion. Those. if a person has a Huinday, then only car_id=1 will be in his field. If someone else has Huinday, then he will also have car_id = 1, not 5.
Another example:

There are duplicate cars in the Car table: LADA (2 times) and BMW (3 times).
In the Human table, people with id 3005, 3006, 3007 have the same car brands (car_id = 7,4,1, these are all BMWs).
And they should have a single car_id, i.e. car_id = 1 (this is a BMW) for id=3005,3006,3007.
That is, remove unnecessary car_id from the Car table if this car has already been seen before.

Similarly, people with id = 3002, 3004 with LADA brands. (car_id for LADA = 3 and 6 from the Car table)
After the query is executed, id=3002 car_id should remain 3, and the person with id=3004 should also have car_id = 3, not 6

Query for Microsoft SQL Server subd.
I wrote a query, but it replaces all car_id with one (as minimum)
I wrote a query that should update the Human table, changing the car_id field there to the minimum of its type (well, if it is LADA, then the minimum is from the set 3, 6).
However, it replaces ALL car_id in the Human table with 1:

update Human set car_id = (
  select min(car_id) from Car c where c.Model in (
    select Model from Car inner join Human on Human.car_id= Car.car_id));

Update the Human car_id table equal to the minimum car_id from the Car table where the car model from the Car table is in the set (select the car brand from the Car table, joining with Human by the common car_id field).
As a result, a table is displayed with ALL brands and their id. Not just one specific model. Accordingly, it takes the very first one in order (which has car_id = 1) and updates all fields and sets them to car_id = 1.
How can I fix this request so that it takes a specific set from car_id for LADA, BMW?
To paraphrase, the question is how to remove duplicates from the parent table Car, which are referenced by the fields of the child table Human by the car_id foreign key. That is, you must first change the car_id from the child table to one of the minimum ones from the corresponding set, and then simply delete the unnecessary ones from the parent table. But my question is exactly how to change the car_id to the minimum.
I hope I was able to clearly explain the essence of the issue.

Answer 1

UPDATE Human
  JOIN Car ON Car.car_id = Human.car_id
  JOIN (
    SELECT model, MIN(car_id) AS car_id
      FROM Car
      GROUP BY model
  ) AS c ON c.model = Car.model
  SET Human.car_id = c.car_id

Answer 2

-- Обновление минимальным кодом:
UPDATE Human
  SET car_id = UniqCar.min_id
  FROM Human 
    INNER JOIN Car ON Human.car_id = Car.car_id 
    INNER JOIN (SELECT MIN(car_id) AS min_id, model
                  FROM Car AS CarMini
                  GROUP BY model) AS UniqCar ON UniqCar.model = Car.model
-- Удаление лишних машин:
DELETE FROM Car
 WHERE Car.car_id <> (SELECT MIN(CarOff.car_id) FROM Car AS CarOff WHERE CarOff.model = Car.model)