Nodes, Branches, and Loops

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# Nodes, Branches, and Loops - PowerPoint PPT Presentation

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

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Presentation Transcript

### Nodes, Branches, and Loops

With an Intro to

Kirchhoff’s Laws

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

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
KCL (cont.)
• For current sources combined in parallel, the current is the algebraic sum of the current supplied by the individual sources.
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
KVL (cont.)
• For voltage sources connected in series, the combined voltage is the algebraic sum of the voltages of the individual sources.
Examples
• Find current io voltage vo in the circuit.
Examples
• Find v1 and v2 in the circuit.