how can we explain that the voltage in parellel branches is equal, as well as the current in series branches is equal.

 

Hello,

Read this chapter of the eBook:
http://www.allaboutcircuits.com/vol_1/chpt_5/index.html

Bertus

 

Ohms Law. Google is your friend

 

Is there a question here I'm missing??

 

Please remember that two or more components are said to be in parallel if the same voltage appears across them. Similarly, two or more components are said to be in series if the same current flows through them. So, your question is essentially understanding the two terms - series and parallel connections.