Nodes, Branches, and Loops

1. Nodes, Branches, and Loops With an Intro to Kirchhoff’s Laws

2. Nodes, Branches, and Loops • Since the elements of a circuit can be interconnected in several ways, it is important to understand the basic concepts of network topology.

3. Branches • A branch represents a single element such as a voltage source or a resistor.

4. Nodes • A node is the point of connection between two or more branches. • Nodes are indicated by a dot in a circuit. If a short circuit connects two nodes, the two nodes constitute a single node.

5. Loops • A loop is any closed path in a circuit. • A loop is a closed path formed by starting at a node, passing through a set of nodes, and returning to the starting node without passing through any node more than once.

6. Topology Theorem • A network with b branches, n nodes, and l independent loops will satisfy the fundamental theorem of network topology: b = l + n - 1

7. Kirchhoff’s Current Law • Kirchhoff’s current law (KCL) states that the algebraic sum of currents entering a node (or closed boundary) is zero. • The sum of the currents entering a node is equal to the sum of the currents leaving the node

8. KCL (cont.) • For current sources combined in parallel, the current is the algebraic sum of the current supplied by the individual sources.

9. Kirchhoff’s Voltage Law • Kirchhoff’s voltage law (KVL) states that the algebraic sum of all voltages around a closed path (or loop) is zero • Sum of voltage drops = Sum of voltage rises

10. KVL (cont.) • For voltage sources connected in series, the combined voltage is the algebraic sum of the voltages of the individual sources.

11. Examples

12. Examples • Find current io voltage vo in the circuit.

13. Examples • Find v1 and v2 in the circuit.