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In electrical engineering, Millman's theorem [1] (or the parallel generator theorem) is a method to simplify the solution of a circuit. Specifically, Millman's theorem is used to compute the voltage at the ends of a circuit made up of only branches in parallel. It is named after Jacob Millman, who proved the theorem.
Indeed, a graph has treewidth at most 2 if and only if it has branchwidth at most 2, if and only if every biconnected component is a series–parallel graph. [4] [5] The maximal series–parallel graphs, graphs to which no additional edges can be added without destroying their series–parallel structure, are exactly the 2-trees.
Figure 1.3. All these topologies are identical. Series topology is a general name. Voltage divider or potential divider is used for circuits of that purpose. L-section is a common name for the topology in filter design. A network with three branches has four possible topologies. Figure 1.4. Series and parallel topologies with three branches
In a series circuit, the current that flows through each of the components is the same, and the voltage across the circuit is the sum of the individual voltage drops across each component. [1] In a parallel circuit, the voltage across each of the components is the same, and the total current is the sum of the currents flowing through each ...
Stephen Cook [1] [2] coined the name "Nick's class" after Nick Pippenger, who had done extensive research [3] on circuits with polylogarithmic depth and polynomial size. [4] Just as the class P can be thought of as the tractable problems (Cobham's thesis), so NC can be thought of as the problems that can be efficiently solved on a parallel ...
[3] [1] [4] Unlike some other paradoxes in science, this paradox is not due to the underlying physics, but to the limitations of the 'ideal circuit' conventions used in circuit theory. [5] The description specified above is not physically realizable if the circuit is assumed to be made of ideal circuit elements , as is usual in circuit theory.
Graphical interpretation of the parallel operator with =.. The parallel operator ‖ (pronounced "parallel", [1] following the parallel lines notation from geometry; [2] [3] also known as reduced sum, parallel sum or parallel addition) is a binary operation which is used as a shorthand in electrical engineering, [4] [5] [6] [nb 1] but is also used in kinetics, fluid mechanics and financial ...
A parallel channel may have additional conductors for other signals, such as a clock signal to pace the flow of data, a signal to control the direction of data flow, and handshaking signals. Parallel communication is and always has been widely used within integrated circuits, in peripheral buses, and in memory devices such as RAM. Computer ...