**Introduction**

Circuits are defined as closed loops through which electrons travel; they are a source of electricity. A circuit may be a parallel circuit or a series circuit; however, hybrid models with other configurations are more popular. In a parallel circuit, the voltage is the same; that is, if a 12-Volt battery is linked parallel to three different bulbs, all three receive 12 volts. In a series circuit, the voltage drops to 4 volts per bulb, as each component takes up 4 volts when the current flows through it.

A circuit is said to be a parallel circuit if two or more components are connected in parallel. No voltage drops occur in such circuits, as the current flows through multiple paths. However, the currents that flow through individual components differ. According to Kirchhoff’s Current Law, the sum of these currents is equal to the total current. The current in each element is found using Ohm’s Law.

Series circuits are known as current-coupled circuits. They are also referred to as daisy chain-coupled circuits (when multiple devices are wired together in a sequence resembling a garland of daisies, it is known as Daisy Chain Scheme). Voltage drops are a defining characteristic of a series circuit. These circuits have only one path through which the current flows; therefore if the line is opened/broken at any point in the series, the entire circuit stops functioning. An apt example of a series circuit is the traditional/older-style Christmas light strings.

**Parallel Circuit Vs. Series Circuit**

A series circuit is a circuit whose components are connected only in a series. The tail end of one component is connected to the head of the next component. On the other hand, a parallel circuit is a circuit whose components have parallel links alone. For example, if a battery is connected to a light bulb that is connected to another bulb, which in turn is connected to another one, and the connection loops back to the battery, it is a series circuit. However, if the bulbs have three different links to the battery, it is a parallel circuit.

**Difference Between Parallel Circuit And Series Circuit In Tabular Form**

Parameters Of Comparison | Parallel Circuit | Series Circuit |

Arrangement of components | In a parallel circuit, the components are parallel to each other and are connected in a head-to-head and tail-to-tail manner (multiple parallel connections). | In a series circuit, the components are arranged in a single line and are connected in a series (head-to-tail manner). |

Current | The total current is equal to the sum of the currents that flow through the circuit’s multiple paths. Current (I) = I _{1} + I_{2} + I_{3} (in a circuit with three parallel connecting lines). | The same current flows through each component. I = I |

Current flow path | Current flows through multiple paths. | Current flows through a single path as it flows from one component to the next. |

Functionality | If one component breaks down, the others will continue to work efficiently, as they are not connected to the damaged component. | If one component breaks down, all the components cease to work, as they are connected to each other. That is, a faulty component will have a cascading/dominoes effect. |

Troubleshooting | Relatively easy to troubleshoot a faulty component. | It is challenging to troubleshoot a series circuit’s faulty component. |

Voltage | The voltage is the same for all components/elements in a parallel circuit. | The total voltage is the sum of the voltage of individual components. V = V1+V2+…+Vn |

Resistance | The total resistance is equal to the reciprocal of the sum of the reciprocal of each component’s resistance. 1 Rtotal = 1R1+1R2+…+1Rn | The total resistance is equal to the sum of each resistance. R = |

**What Is Parallel Circuit?**

In a parallel circuit, as the voltage is the same for the entire circuit, the total current is divided and supplied to different branches; this results in varying amounts of current flowing through each resistor/component. Most lithium-ion rechargeable batteries like laptop batteries are linked in parallel. Another example of a parallel circuit is a house’s wiring system. A single power source supplies current to all the appliances within the house; each appliance receives the same voltage. The total current in a parallel circuit is equal to the summation of the current that flows through each resistor. Alternatively, it is calculated using the following formula:

*I**total**=V**1**R**1**+**1**R**2**+…+**1**R**n*

In a parallel circuit, the voltage is the same for all components, as each component is separately connected to the power source. Therefore,

*V=**V**1**+**V**2**+…+**V**n*

An object’s electrical resistance (or simply resistance) is a measure of its opposition to current flow. Resistance is defined as the ratio of voltage to the current that flows through an object. Usually, resistance and conductance are constant, as the current is directly proportional to voltage according to Ohm’s law. However, when they are not proportional, the value of resistance varies. The following formula is used to find out individual resistance:

*R= **V**I*

The total resistance is found by calculating the sum of the reciprocals of resistance found using Ohm’s law and taking the reciprocal of such a sum. When only two resistors are present in the circuit the formula becomes less complicated (the mnemonic *product over sum* aids in remembering the variation). For a circuit with *n* number of resistors,

*1**R**total**=**1**R**1**+**1**R**2**+…+**1**R**n*

If only two resistors are present,

*R**total**=**R**1**R**2**R**1**+**R**2*

An excellent example of parallel resistance is the human circulatory system. The total resistance is determined by adding the reciprocals of the renal, hepatic, and other arteries and finding the reciprocal of the sum. An object’s material determines its resistance level. Those made of electrical insulators have low conductance and extremely high resistance, while those made of electrical conductors have high conductance and low resistance.

Conductors are the objects through which the current flows, and conductance measure the ease with which the current flows. The total conductance of a parallel circuit is equal to the sum of each component’s conductance.

*G= **G**1**+**G**2**+…+**G**n*

Inductors, also known as choke or coils, are typically insulated wires wound into a coil. They store magnetic energy when the current flows through them. Total inductance (L) is the ratio of voltage to the rate of change of current and is calculated as follows:

*1**L**total**=**1**L**1**+**1**L**2**+…+**1**L**n*

The capacitors store electrical energy created by electric charges in a circuit. The capacitance of a parallel circuit is determined by adding the individual capacitances.

*C**total**=**C**1**+**C**2**+…+**C**n*

A switch connects a circuit’s conducting path (when it is on) or disconnects it (when it is off). A circuit’s switch does not function like a door. In circuits, the switches are on when they are closed (current flows through the circuit), and it means they are off if one says they are open (current does not flow through the circuit). This type of jargon may throw off people who never bothered their heads about circuits before; however, it is pretty easy to remember once they understand how a circuit switch works.

In a parallel circuit, two or more switches are in parallel; therefore, current flows through the circuit even if one switch remains closed. A single malfunctioning component or open switch will not bring down the entire circuit. A parallel circuit’s switches follow the logical OR. According to logical OR, a set of operands are false only if all of its operands are false. When applied to circuit switches, this means the current flow will stop only if all the switches are open/off.

**What Is Series Circuit?**

A series circuit consists of cells and batteries, resistance units, inductors, capacitors, and switches. All these components are connected in a series that loops back to the batteries. Therefore, the current flows in a single path resulting in voltage drops. The total voltage of a series circuit is equal to the sum of the voltage of individual resistors. Alternatively, it can be calculated by multiplying the total current with the sum of the individual resistance units. That is,

V = I *R**1**+**R**2**+…+**R**n*

The SI unit of resistance/electrical resistance is â„¦ (ohm), and the total resistance in a series circuit is the sum of the individual resistances. Therefore,

*R**total**= **R**1**+**R**2**+…+**R**n*

The level of resistance depends on the object’s shape and size (apart from the material). The longer and thinner the wire, the higher the resistance. On the other hand, a short or thick wire will have low resistance. The arrangement of blood vessels in an organ is an example of a series circuit. The arteries, arterioles, and capillaries are the resistors. Total resistance is equal to the sum of each resistance. That is,

*R**total**=**R**arteries**+**R**arterioles**+**R**capillaries*

Electrical conductance is the reciprocal of electrical resistance. The SI unit of conductance is Siemens (S), formerly referred to as ‘mho’). Therefore, the total conductance (G) can be calculated as follows:

*G**total**=**1**G**1**+**1**G**2**+…+**1**G**n*

In some rare cases, two conductors are in a series circuit. In such cases,

*G**total**=**G**1**G**2**G**1**+**G**2*

The total inductance (L) is equal to the sum of the non-coupled individual inductors. Sometimes, the magnetic field of one inductor couples with another. This coupling results in mutual inductance. Mutual inductance can also occur within an inductor – this is termed Self-inductance. In a series circuit with three coils/inductors, there are three self-inductances or simply inductances *M**11**,**M**22**,**M**33* in addition to the six possible mutual inductances*M**12**,**M**13**,**M**23** and **M**21**,**M**31**,**M**32*. Therefore,

*L**total**=**M**11**+**M**22**+**M**33**+**M**12**+**M**13**+**M**23**+**M**21**+**M**31**+**M**32*

The formula can be conveniently extended for any number of coils with mutual inductances.

The total capacitance of a series circuit is equal to the sum of the elastance (the reciprocal of capacitance) of each capacitor. If even one switch in a series circuit is open, the entire circuit will stop functioning. A series circuit’s switches follow the logical AND. According to logical AND, a set of operands is true only if all of its operands are true. In the case of circuit switches, the current stops flowing if all the switches are not closed/on. That is, a single open switch prevents the circuit from functioning effectively.

**Main Difference Between Parallel Circuit And Series Circuit In Points**

- In a series circuit, the current that courses through each element is the same; therefore, the total current (I) is equal to the current that passes through each component (I = I
_{1}= I_{2}= I_{3}and so on). On the other hand, the total current in a parallel circuit is calculated by summating the currents flowing through each element. - The voltage differs in a series circuit (as voltage drops occur). Therefore, the total voltage is equal to the sum of the voltage drops across individual components. In a parallel circuit, the voltage is the same.
- A parallel circuit’s switch follows the logical OR, whereas a series circuit’s switch follows the logical AND.
- A series circuit is busted if even one component short-circuits/becomes faulty or the series breaks. However, a parallel circuit does not suffer from such issues, as each component has its own circuit in the form of parallel links. Therefore, only the damaged component will not function; the others will function perfectly.
- Detecting and troubleshooting a fault in series circuits is highly challenging, whereas it is comparatively easier to find the root cause of a problem in a parallel circuit.
- The total resistance in a series circuit is greater than the highest individual resistance value. On the other hand, the total resistance in a parallel circuit is always lesser than the smallest individual resistance value.

**Conclusion**

Simply put, both circuits are similar except for the fact that the role of Voltage and Current is exchanged. In a parallel circuit, no voltage drops occur, but the current flow differs, whereas, in a series circuit, the current is the same, but voltage drops occur. Moreover, in a parallel circuit, only a fraction of the total current flows through each path. In a series circuit, only a fraction of the total voltage passes through each component. For example, two 12-volt batteries (connected in a series) are required to power a 24-volt system in some trucks.

A circuit with two branches can only be a parallel or series circuit. However, if the circuit has three branches, the possible topology increases to four (series, parallel, parallel-series, and series-parallel). However, many other topologies exist, and the possibilities are endless. Nowadays, complex combinations of series and parallel circuits and other configurations are used.

**References**

- https://en.wikipedia.org/wiki/Series_and_parallel_circuits
- https://www.javatpoint.com/series-vs-parallel-circuits
- https://en.wikipedia.org/wiki/Electrical_conductance
- https://en.wikipedia.org/wiki/Switch
- https://en.wikipedia.org/wiki/Logical_conjunction
- https://en.wikipedia.org/wiki/Logical_disjunction
- https://circuitglobe.com/difference-between-series-and-parallel-circuit.html
- https://en.wikipedia.org/wiki/Topology_(electrical_circuits)
- https://en.wikipedia.org/wiki/Inductor