Before I get too far into the weeds discussing circuit analysis or design techniques I wanted to take some time to define two terms which you will commonly encounter when reading about or discussing circuits. These two terms are Nodes and Branches and are an easy way to describe the various components and connections in a circuit. In the future an intuitive understanding of these two concepts will be central to techniques like Nodal and Mesh analysis.
Simply put, a Node is any connection between two or more components and a Branch is any component placed between two nodes in a circuit. To clarify this I have highlighted the nodes and branches on the following series circuit:
Here we can see the four Nodes marked with red circles at the points where each of the components are connected. The four Branches then would be the components themselves (R1, R2, C1 and the battery). It’s important to note that a branch can be any component whether it’s a power supply, a load, resistor, capacitor, inductor or anything else which is included in the circuit. Easy enough right!
If we move the components around slightly to make the following parallel circuit things can get slightly less intuitive :
Upon initial investigation of this circuit you may say that the circuit has 8 nodes, four on the top and four at the bottom. This is a natural response however it is a symptom of the way we draw circuits rather than the physical components of the circuit it is describing. If you look along the top and bottom you will see that there are no components between the positive terminal of the battery and the three other components. This means when building this circuit you would actually just connect the terminals of the three other components together on either side of the battery. Since all four components are connected together in parallel there are in fact only two Nodes as shown above. Since there are still four components these still represent the 4 branches of the circuit.