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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 ]
In electrical engineering, the parallel operator can be used to calculate the total impedance of various serial and parallel electrical circuits. [nb 2] There is a duality between the usual (series) sum and the parallel sum. [7] [8]
The following table gives formula for the spring that is equivalent to a system of two springs, in series or in parallel, whose spring constants are and . [1] The compliance c {\displaystyle c} of a spring is the reciprocal 1 / k {\displaystyle 1/k} of its spring constant.)
A network with two components or branches has only two possible topologies: series and parallel. Figure 1.2. Series and parallel topologies with two branches. Even for these simplest of topologies, the circuit can be presented in varying ways. Figure 1.3. All these topologies are identical. Series topology is a general name.
That means an ideal voltage source is replaced with a short circuit, and an ideal current source is replaced with an open circuit. Resistance can then be calculated across the terminals using the formulae for series and parallel circuits. This method is valid only for circuits with independent sources.
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 ...
The current entering any junction is equal to the current leaving that junction. i 2 + i 3 = i 1 + i 4. This law, also called Kirchhoff's first law, or Kirchhoff's junction rule, states that, for any node (junction) in an electrical circuit, the sum of currents flowing into that node is equal to the sum of currents flowing out of that node; or equivalently:
Most analysis methods calculate the voltage and current values for static networks, which are circuits consisting of memoryless components only but have difficulties with complex dynamic networks. In general, the equations that describe the behaviour of a dynamic circuit are in the form of a differential-algebraic system of equations (DAEs).