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Many circuits can be analyzed as a combination of series and parallel circuits, along with other configurations. 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 ]
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.
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.
If the network is particularly simple or only a specific current or voltage is required then ad-hoc application of some simple equivalent circuits may yield the answer without recourse to the more systematic methods. Nodal analysis: The number of voltage variables, and hence simultaneous equations to solve, equals the number of nodes minus one ...
Series and parallel are, in fact, the 2-terminal versions of star and polygon topology. A common simple topology that cannot be solved by series and parallel combinations is the input impedance to a bridge network (except in the special case when the bridge is in balance). [9]
For a parallel RLC circuit, the Q factor is the inverse of the series case: [21] [20] = = = [22] Consider a circuit where R, L, and C are all in parallel. The lower the parallel resistance is, the more effect it will have in damping the circuit and thus result in lower Q. This is useful in filter design to determine the bandwidth.
Now each problem is relatively simple, since it involves only one single ideal current source. To obtain exactly the same outcome voltages at the nodes for each problem, the equivalent resistances in the two circuits must be the same, this can be easily found by using the basic rules of series and parallel circuits: