How did the relationship between Britain and its colonies change after the war, and why did Britain seek to change those relationships?

Since you don’t specify to which war you are referring, I assume you are referring to the French and Indian War. After the French and Indian War, the relationship began to change between Great Britain and the thirteen colonies.

One reason why the British established colonies was because they wanted to benefit economically from their colonies. After the French and Indian War, the colonies were becoming more expensive to operate, which meant the British were making less money from the colonies. Thus, the British wanted the colonists to share in some of the expenses of running the colonies because the colonists were benefiting from the rule of British. For example, the British army was protecting the colonists from attacks by the Native Americans. The British felt it was reasonable to have the colonists pay for housing the British troops that were in the colonies to protect them.

Another example of how the relationship changed was that the British began to pass tax laws that created taxes that the colonists had to pay. The Stamp Act and the Townshend Acts were examples of new tax laws. The colonists felt these tax laws were unfair because they didn’t have representatives in Parliament that could speak about or vote on these tax laws.

The changing relationship ultimately led the colonists to decide they needed to be free from British rule. This led to the writing of and adopting of the Declaration of Independence.