обязанныйпричастие прошедшего времени Полная форма страдательного причастия прошедшего времени от глагола «обязать»
boundSlightly more formal; emphasizes being firmly obligated (often by rules, a promise, or a contract). Она — обязанная выполнить обещание.
She is bound to keep her promise.
indebtedUsed for owing money or a debt; also possible figuratively for owing gratitude (then usually 'to'). Он — обязанный банку заемщик.
He is an indebted borrower.
liableLegal/official: under an obligation according to law or rules. Граждане, обязанные являться на выборы, получили уведомления.
Citizens liable to attend the elections received notices.
obligedCommon for being under a duty/requirement; often followed by an infinitive. Каждый обязанный вернуть долг должен сделать это до конца месяца.
Everyone obliged to repay the debt must do so by the end of the month.
owingUsed for something being due to a cause or help; typically followed by 'to'. Своим успехом он был обязанный поддержке друзей.
He was owing his success to his friends' support.
duty-boundEmphasizes a strong moral duty; stylistically elevated.