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 that flows through each of the components is the same, and the
Consider a very simple circuit consisting of four light bulbs and a 12-volt
In a series circuit, every device must function for the circuit to be complete. If one bulb burns out in a series circuit, the entire circuit is broken. 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 referred to as current-coupled or
A series circuit 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.
In a series circuit, the voltage is the sum of the voltage drops of the individual components (resistance units).
The total resistance of resistance units in series is equal to the sum of their individual resistances:
Rs=>Resistance in series
For a special case of two resistances 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 coupled 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.