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Nodes, Branches, and LoopsPowerPoint Presentation

Nodes, Branches, and Loops

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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.

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