Mam obowiązek wobec rodziny.

Mam means I have. It is the 1st person singular present tense form of the verb mieć (to have).

So:

• mieć = to have
• mam = I have

Here obowiązek is the direct object of mam, so grammatically it is in the accusative case.

However, obowiązek is a masculine inanimate noun, and in Polish, many masculine inanimate nouns have the same form in the nominative and accusative singular.

So:

• nominative: obowiązek
• accusative: obowiązek

The case does change in function, but not in spelling.

Obowiązek means duty, obligation, or responsibility, depending on context.

In this sentence, it suggests a fairly serious sense of duty, not just a casual task. It can sound moral, social, or personal.

For example:

• mam obowiązek = I have a duty / I am obliged
• to mój obowiązek = it is my duty

Wobec means something like toward, to, in relation to, or with respect to.

In this sentence, it shows who the duty is directed toward.

So wobec rodziny means:

• toward the family
• to the family
• in relation to the family

In English, we often would not translate it word-for-word, but in Polish it is a very natural way to express this relationship.

Because wobec requires the genitive case.

The basic dictionary form is:

• rodzina = family

But after wobec, it changes to the genitive:

• wobec rodziny

So:

• nominative: rodzina
• genitive: rodziny

This is a very important thing to learn with Polish prepositions: many of them require a specific case.

Not necessarily. Polish often leaves out possessive words like my when the meaning is obvious from context.

So:

• Mam obowiązek wobec rodziny. = I have a duty to my/the family, depending on context
• Mam obowiązek wobec mojej rodziny. = I have a duty to my family

Adding mojej makes it more explicit. Without it, the sentence can still naturally refer to one's own family if that is clear from the situation.

It is natural, but it sounds a bit formal or serious.

Why?

• obowiązek is a weighty word
• wobec is slightly more formal than some other ways of expressing relationships

So this sounds like something you might see in:

• serious conversation
• writing
• moral or legal discussion
• reflective speech

It is not wrong in everyday speech, but it is not especially casual.

Yes. That changes the meaning slightly.

• Mam obowiązek wobec rodziny. = I have a duty/obligation toward my family
  This sounds more general or abstract, as if speaking about one important obligation.
• Mam obowiązki wobec rodziny. = I have duties/obligations toward my family
  This emphasizes multiple responsibilities.

Both are correct. The singular often sounds more like a general sense of duty, while the plural stresses several concrete responsibilities.

They are related, but not the same.

• muszę = I must
• mam obowiązek = I have a duty / I am obliged

Muszę usually focuses on necessity: something has to be done.

Mam obowiązek focuses more on responsibility, duty, or moral/social obligation.

Compare:

• Muszę pomóc rodzinie. = I must help my family.
• Mam obowiązek wobec rodziny. = I have a duty toward my family.

So mam obowiązek sounds more reflective and value-based.

No, Polish word order is fairly flexible, but different orders change the emphasis.

The neutral order is:

• Mam obowiązek wobec rodziny.

You could also say:

• Wobec rodziny mam obowiązek.

That is grammatical, but it sounds more marked, as if you are emphasizing toward the family.

For learners, the original version is the safest and most natural neutral order.

Because wobec is the natural preposition for expressing duty/attitude/responsibility toward someone.

• wobec rodziny = toward the family
• dla rodziny usually means for the family
• do rodziny usually means to the family in the sense of direction, not duty

So:

• mam obowiązek wobec rodziny = correct and natural
• mam obowiązek dla rodziny = not the normal way to say this
• mam obowiązek do rodziny = incorrect in this meaning

This is one of those combinations that is best learned as a set phrase:

• obowiązek wobec kogoś/czegoś = duty toward someone/something