Final answer:
The House of Hanover was the royal family during Jane Austen's time. George III was the king during the American Revolution.
Step-by-step explanation:
The royal family that was going on during Jane Austen's time was the House of Hanover. After the death of Queen Anne, the English Crown passed to the nearest Protestant relatives of the Stuarts, the Electors of Hanover, and George I became the first Hanoverian monarch of England. His grandson, George III, was the king during the time of the American Revolution.