I am reading about Hurwitz's theorem
``Let $\varphi : C' \to C$ be a surjective morphism of irreducible smooth projective curves over $k$ of genus $g(C')$ and $g(C)$. Then we have $$2g(C') - 2 = \deg (\varphi ) (2g(C) - 2) + \deg (R_{\varphi}) $$ where $R_{\varphi}$ is the ramification divisor of $\varphi$.''
However, I haven't yet understood really about the ramification divisor and I had some difficulties to determinate $R_{\varphi}$. In particular, if $C' \equiv C \equiv \mathbb{P^1}$ then $R_{\varphi} = \sum\limits_{x \in C'} (e_x -1)$. Is this true?
My question: How is the dependence of the ramification divisor of surjective morphism to its ramification indexes?
Thank you very much!