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Encyclopedia > Parallel circuits
Series (left) and parallel (right) circuits with two resistors and measurements of voltage and current.

Electrical circuit components can be connected together in one of two ways: series or parallel. These two names describe the method of attaching the components, that is one after the other or next to each other. If two or more circuit components are connected end to end like a daisy chain, it is said they are connected in series. A series circuit is a single path for current through all of its components. If two or more circuit components are connected like the rungs of a ladder it is said they are connected in parallel. A parallel circuit is a different path for current through each of its components. A parallel circuit provides the same voltage across all its components. Image File history File links Series_and_parallel_circuits. ... Image File history File links Series_and_parallel_circuits. ... An electrical network or electrical circuit is an interconnection of analog electrical elements such as resistors, inductors, capacitors, diodes, switches and transistors. ... International safety symbol Caution, risk of electric shock (ISO 3864), colloquially known as high voltage symbol. ...

As an example, consider a very simple circuit consisting of two lightbulbs and one 9 V battery. If a wire joins the battery to one bulb, to the next bulb, then back to the battery, in one continuous loop, the bulbs are said to be in series. If each bulb is wired to the battery in a separate loop, the bulbs are said to be in parallel. If the two lightbulbs are connected in series the same current flows in both of them; each lightbulb experiences about 4.5 V. If the two lightbulbs are connected in parallel the currents flowing in the two lightbulbs combine to form the current flowing in the battery; each lightbulb experiences 9 V. Symbols representing a single Cell (top) and Battery (bottom), used in circuit diagrams. ...

## Contents

Series circuits are sometimes called cascade-coupled or daisy chain-coupled. The current that flows in a series circuit has to flow through every component in the circuit. Therefore, all components in a series connection carry the same current. The elementary meaning of daisy chain is a garland created from the daisy flower, generally as a childrens game. ... In electricity, current refers to electric current, which is the flow of electric charge. ...

### Resistors

To find the total resistance of all the components, add the individual resistances of each component: Electrical resistance is a measure of the degree to which an electrical component opposes the passage of current. ...

Image File history File links This is a lossless scalable vector image. ...

for components in series with resistances R1, R2, etc. To find the current I, use Ohm's law: A voltage source, V, drives an electric current, I , through resistor, R, the three quantities obeying Ohms law: V = IR Ohms law states that, in an electrical circuit, the current passing through a conductor between two points is proportional to the potential difference (i. ...

.

To find the voltage across a component with resistance Ri, use Ohm's law again: International safety symbol Caution, risk of electric shock (ISO 3864), colloquially known as high voltage symbol. ...

where I is the current, as calculated above. The components divide the voltage according to their resistances, so, in the case of two resistors,

.

### Inductors

Inductors follow the same law, in that the total inductance of non-coupled inductors in series is equal to the sum of their individual inductances: An inductor is a passive electrical device employed in electrical circuits for its property of inductance. ... An electric current i flowing around a circuit produces a magnetic field and hence a magnetic flux Î¦ through the circuit. ...

Image File history File links Inductors_in_series. ...

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 you have two inductors in series, there are two possible equivalent inductances:

or

,

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 M12, M13, M23 and M21, M31 and M32. There are also the three self-inductances of the three coils: M11, M22 and M33.

Therefore

Ltotal = (M11 + M22 + M33) + (M12 + M13 + M23) + (M21 + M31 + M32)

By reciprocity Mij = Mji 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 mututal 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.

### Capacitors

Capacitors follow a different law. The total capacitance of capacitors in series is equal to the reciprocal of the sum of the reciprocals of their individual capacitances: See Capacitor (component) for a discussion of specific types. ... Capacitance is a measure of the amount of electric charge stored (or separated) for a given electric potential. ... The reciprocal function: y = 1/x. ...

Image File history File links This is a lossless scalable vector image. ...

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The working voltage of a series combination of identical capacitors is equal to the sum of voltage ratings of individual capacitors provided that equalizing resistors are used to ensure equal voltage division. This is all because of Ohm's law.

## Parallel circuits

If two or more components are connected in parallel they have the same potential difference (voltage) across their ends. The potential differences across the components are the same in magnitude, and they also have identical polarities. Hence, the same voltage is applicable to all circuit components connected in parallel. The total current I is the sum of the currents through the individual components, in accordance with Kirchhoff's Current Law. The current in each individual resistor is found by Ohm's Law. Factoring out the voltage gives International safety symbol Caution, risk of electric shock (ISO 3864), colloquially known as high voltage symbol. ... Kirchhoffs circuit laws are a pair of laws that deal with the conservation of charge and energy in electrical circuits, and were first described in 1845 by Gustav Kirchhoff. ... A voltage source, V, drives an electric current, I , through resistor, R, the three quantities obeying Ohms law: V = IR Ohms law states that, in an electrical circuit, the current passing through a conductor between two points is proportional to the potential difference (i. ...

.

### Notation

The parallel property can be represented in equations by two vertical lines (as in geometry) to simplify the equations. Parallel is a term in geometry and in everyday life that refers to a property in Euclidean space of two or more lines or planes, or a combination of these. ...

### Resistors

To find the total resistance of all components, add the reciprocals of the resistances Ri of each component and take the reciprocal of the sum: Electrical resistance is a measure of the degree to which an electrical component opposes the passage of current. ... Look up reciprocal in Wiktionary, the free dictionary. ...

Image File history File links This is a lossless scalable vector image. ...

.

To find the current in a component with resistance Ri, use Ohm's law again: In electricity, current refers to electric current, which is the flow of electric charge. ...

.

The components divide the current according to their reciprocal resistances, so, in the case of two resistors,

.

### Inductors

Inductors follow the same law, in that the total inductance of non-coupled inductors in parallel is equal to the reciprocal of the sum of the reciprocals of their individual inductances: An inductor is a passive electrical device employed in electrical circuits for its property of inductance. ... An electric current i flowing around a circuit produces a magnetic field and hence a magnetic flux Î¦ through the circuit. ...

Image File history File links Inductors_in_parallel. ...

.

If the inductors are situated in each other's magnetic fields, this approach is invalid due to mutual inductance. If the mutual inductance between two coils in parallel is M, the equivalent inductor is:

If L1 = L2

The sign of M depends on how the magnetic fields influence each other. For two equal tightly coupled coils the total inductance is close to that of each single coil. If the polarity of one coil is reversed so that M is negative, then the parallel inductance is nearly zero or the combination is almost non-inductive. We are assuming in the "tightly coupled" case M is very nearly equal to L. However, if the inductances are not equal and the coils are tightly coupled there can be near short circuit conditions and high circulating currents for both positive and negative values of M, which can cause problems.

More than 2 inductors becomes more complex and the mutual inductance of each inductor on each other inductor and their influence on each other must be considered. For three coils, there are three mutual inductances M12, M13 and M23. This is best handled by matrix methods and summing the terms of the inverse of the L matrix (3 by 3 in this case).

The pertinent equations are of the form:

### Capacitors

Capacitors follow a different law. The total capacitance of capacitors in parallel is equal to the sum of their individual capacitances: See Capacitor (component) for a discussion of specific types. ... Capacitance is a measure of the amount of electric charge stored (or separated) for a given electric potential. ...

Image File history File links This is a lossless scalable vector image. ...

.

The working voltage of a parallel combination of capacitors is always limited by the smallest working voltage of an individual capacitor.

A Wheatstone bridge is a measuring instrument invented by Samuel Hunter Christie in 1833 and improved and popularized by Sir Charles Wheatstone in 1843. ... The Y-Î” transform (also written Y-delta or Wye-delta), Kennellys delta-star transformation, star-mesh transformation or T-Î  (or T-pi) transform is a mathematical technique to simplify analysis of an electrical network. ... In electronics, a voltage divider is a simple device designed to create a voltage (Vout) which is proportional to another voltage (Vin). ... The Current Divider (or division) rule (Sometimes referred to a CDR) is used to find the current flowing through an impedance or other circuit when it is connected in parallel with another impedance. ... Electrical impedance, or simply impedance, is a measure of opposition to a sinusoidal alternating electric current. ... Results from FactBites:

 Edison, Thomas [encyclopedia] (1411 words) Jumbo dynamos, with drum-wound armatures, could maintain 110 volts with 90 percent efficiency. The three-wire system, first installed in Sunbury, Pennsylvania, in 1883, superseded the parallel circuit, used 110 volts, and necessitated high-resistance lamp filaments (metal alloys were later used). In 1883 Edison made a significant discovery in pure science, the Edison effect.electrons flowed from incandescent filaments.
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