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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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Nodes branches and loops

Nodes, Branches, and Loops

With an Intro to

Kirchhoff’s Laws


Nodes branches and loops1
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
Branches

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


Nodes
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
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
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

  • 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
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

  • 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
KVL (cont.)

  • For voltage sources connected in series, the combined voltage is the algebraic sum of the voltages of the individual sources.



Examples1
Examples

  • Find current io voltage vo in the circuit.


Examples2
Examples

  • Find v1 and v2 in the circuit.


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