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A series circuit with a voltage source (such as a battery, or in this case a cell) and three resistance units. Two-terminal components and electrical networks can be connected in series or parallel. The resulting electrical network will have two terminals, and itself can participate in a series or parallel topology.
Series RL, parallel C circuit with resistance in series with the inductor is the standard model for a self-resonant inductor. A series resistor with the inductor in a parallel LC circuit as shown in Figure 4 is a topology commonly encountered where there is a need to take into account the resistance of the coil winding and its self-capacitance.
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.
These include resistors in series, resistors in parallel and the extension to series and parallel circuits for capacitors, inductors and general impedances. Also well known are the Norton and Thévenin equivalent current generator and voltage generator circuits respectively, as is the Y-Δ transform. None of these are discussed in detail here ...
If all circuit components were linear or the circuit was linearized beforehand, the equation system at this point is a system of linear equations and is solved with numerical linear algebra methods. Otherwise, it is a nonlinear algebraic equation system and is solved with nonlinear numerical methods such as Root-finding algorithms.
The expression series-parallel can apply to different domains: Series and parallel circuits for electrical circuits and electronic circuits; Series-parallel partial order, in partial order theory; Series–parallel graph in graph theory; Series–parallel networks problem, a combinatorial problem about series–parallel graphs
The equivalent resistance R th is the resistance that the circuit between terminals A and B would have if all ideal voltage sources in the circuit were replaced by a short circuit and all ideal current sources were replaced by an open circuit (i.e., the sources are set to provide zero voltages and currents).
parallel – series (circuits) resistance – conductance; ... The use of duality in circuit theory is due to Alexander Russell who published his ideas in 1904. [1] [2]