Hello. I am having some trouble figuring out when a possessive pronoun should be used instead of a personal pronoun. Thanks!
That's a pretty open question. Maybe you could give us some context, so that we can explain it to you better.
But, well... what exactly you don't understand? a possessive pronoun is a possessive pronoun. Try thinking in English: You don't say : "She cat is black" or "I car is very big", but rather "her cat is black" and "my car is very big"
The same works for german. "ihre Katze ist schwarz" und "mein Auto ist sehr groß"
The examples you have given are of possessive adjectives, not possessive pronouns. Not "Her cat is black" but "Hers is black". Not "My car is very big" but "Mine is very big". Cat and car are understood from context. Like any pronoun, possessive pronouns replace nouns. They have the added feature of indicating that the replaced noun is owned by someone and who the owner is. If no ownership is stated, use the personal pronouns. Unlike in English, in German the possessive pronouns and adjectives are identical. "Ihre Katze ist schwarz", "Ihre ist schwarz". "Mein Auto ist sehr groß", "Mein ist sehr groß".
Unlike in English, in German the possessive pronouns and adjectives are identical. "Ihre Katze ist schwarz", "Ihre ist schwarz". "Mein Auto ist sehr groß", "Mein ist sehr groß".
That's not quite true -- as your second example shows, where it should be Meins ist sehr groß. (Or Meines.)
Possessive pronouns and adjectives are mostly the same in German but not completely.
The main difference I can think of is that the pronouns always have gender and case endings, while the possessive adjectives sometimes do not (in the cases where the indefinite article is simply ein without ending, i.e. masculine/neuter nominative as well as neuter accusative).
Similarly, Mein Vater ist alt, Meiner ist alt.