Series and parallel circuits
Components of an
A circuit composed solely of components connected in series is known as a series circuit; likewise, one connected completely in parallel is known as a parallel circuit.
In a series circuit, the current through each of the components is the same, and the
Consider a very simple circuit consisting of four light bulbs and one 6 V
In a series circuit, every device must function for the circuit to be complete. One bulb burning out in a series circuit breaks the circuit. In parallel circuits, each light bulb has its own circuit, so all but one light could be burned out, and the last one will still function.
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Series circuits are sometimes called current-coupled or
A series circuit's principle characteristic is that it has only one path in which its current can flow. Opening or breaking a series circuit at any point
In a series circuit the current is the same for all of the elements.
The total resistance of resistors in series is equal to the sum of their individual resistances:
For a special case of two resistors in series, the total conductance is equal to:
However, in some situations it is difficult to prevent adjacent inductors from influencing each other, as the magnetic field of one device couples with the windings of its neighbours. This influence is defined by the mutual inductance M. For example, if two inductors are in series, there are two possible equivalent inductances depending on how the magnetic fields of both inductors influence each other.
When there are more than two inductors, the mutual inductance between each of them and the way the coils influence each other complicates the calculation. For a larger number of coils the total combined inductance is given by the sum of all mutual inductances between the various coils including the mutual inductance of each given coil with itself, which we term self-inductance or simply inductance. For three coils, there are six mutual inductances , , and , and . There are also the three self-inductances of the three coils: , and .
By reciprocity = so that the last two groups can be combined. The first three terms represent the sum of the self-inductances of the various coils. The formula is easily extended to any number of series coils with mutual coupling. The method can be used to find the self-inductance of large coils of wire of any cross-sectional shape by computing the sum of the mutual inductance of each turn of wire in the coil with every other turn since in such a coil all turns are in series.
In a series circuit the voltage is addition of all the voltage elements.