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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 ]
A general formula for the current I X in a resistor R X that is in parallel with a combination of other resistors of total resistance R T (see Figure 1) is [1] = +, where I T is the total current entering the combined network of R X in parallel with R T.
The number of series and parallel combinations that can be formed grows exponentially with the number of resistors, n. For large n the size of the set has been found by numerical techniques to be approximately 2.53 n and analytically strict bounds are given by a Farey sequence of Fibonacci numbers . [ 1 ]
A resistor network that is a combination of parallel and series connections can be broken up into smaller parts that are either one or the other. Some complex networks of resistors cannot be resolved in this manner, requiring more sophisticated circuit analysis. Generally, the Y-Δ transform, or matrix methods can be used to solve such problems.
In an ideal case, cross-section and physical composition of the examined material are uniform across the sample, and the electric field and current density are both parallel and constant everywhere. Many resistors and conductors do in fact have a uniform cross section with a uniform flow of electric current, and are made of a single material ...
At each stage, resistors for the "rung" and "leg" are chosen so that the rung value matches the leg value plus the equivalent resistance of the previous rungs. The rung and leg resistors can be formed by pairing other resistors in series or parallel in order to increase the number of available combinations. This process can be automated.
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.
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 ...