Parallel Circuits

A parallel circuit is where the electric current has multiple paths to flow through. It has two or more paths for current flow. Parallel circuits are one of the two types of circuits in which the devices have a common ending point making them appear to be in parallel. In this article, we will study these types of circuits through their circuit diagram and their working. We will also discuss the characteristics of such circuits. To give some real-life applications of these circuits, we will discuss the advantages and disadvantages of such circuits. We will also build the base for readers through some solved examples. In the end, we will compare parallel circuits with another kind of circuits i.e. series circuits, and will conclude the article.

What are Parallel Circuits ?

Parallel circuits are a kind of circuit in which current emerges from a node and branches off to different paths which eventually meet up at a common node. Due to the branching, the path appears to be in parallel thereby giving it the name parallel circuits. Due to the branching, different current flows in each branch but it is important to note that each branch has the same potential difference which is equal to the potential drop between the two node points.

In these circuits, First, the current is branched out and then it is recombined at the common point. In a parallel circuit, elements are not connected end-to-end.

Key Principles of Parallel Circuit

Here are the three key principles of laws of the parallel circuit:

1. Voltage : Voltage in a parallel circuit plays an important role. All components share the same voltage. This means that in any branch of a parallel circuit, the voltage drop is the same.
2. Resistance : Resistances diminish to equal a smaller, total resistance. This means that the overall resistance of the circuit becomes smaller with the addition of more components resulting in a smaller overall resistance.
3. Current : Branch currents add together to equal a larger, total current. This means that when we add the current of an individual branch of the circuit, we get an overall larger current in the circuit. Using Ohm’s Law for Parallel Circuits to Determine Current 

Working of Parallel Circuit

The parallel circuit looks like any other circuit with the addition of branching as shown below :

Parallel Circuit

In a parallel circuit, the current flowing in the circuit is equal to the sum of current in the individual branch. We will apply this in the above circuit.

Hence I=I₁+I₂+I₃

Since the voltage across each branch is the same we write I=V/R_i

I=V/R₁+V/R₂+V/R₃

Let R_eq be the equivalent Resistance of the circuit then

V/R_eq=V/R₁+V/R₂+V/R₃

1/R_eq=1/R₁+1/R₂+1/R₃

Hence equivalent resistance of the circuit is

1/R_eq=1/R₁+1/R₂+1/R₃

Characteristics of Parallel Circuits

Some characteristics of parallel circuits are mentioned below:

• Instead of being connected end-to-end, each device joins the same two spots i.e. there are two common nodes where each branch starts and ends. Between these two common points, there can be multiple branches
• Voltage is the same across each branch of the parallel circuit equal to the potential drop between the two nodes.
• The sum of the currents through each branch is equal to the total current that flows from the source. This means current I=I₁+I₂+…………..I_n.
• The Total circuit resistance decreases as the number of branches increases. This can be shown mathematically, equivalent resistance of a parallel circuit is less than the smallest individual resistance in the circuit.
• Each component in a parallel circuit works on its own i.e. it operates independently. If one component gets damaged or is removed, the others will continue to function without having any effect.

Advantages of Parallel Circuits

The advantages of parallel circuits are:

• Independent Components: In a parallel circuit, all components operate independently. Since the components have an independent voltage they work even when a component in any other branch is not working.
• Different Current Distribution: In the real world, every appliance has its current requirement depending on its rating. In a parallel circuit, every branch may have a different current flowing through it thereby allowing different current distribution.
• Stable Voltage: Each device in a parallel circuit receives constant voltage, this stable running voltage is the same across each branch ensuring a stable circuit.
• Low Resistance: In a parallel circuit, the equivalent resistance is less than the smallest individual resistance. As we know current is inversely proportional to resistance, This can result in increased current flow, hence being useful when a high current is required.
• Low Complexity: Parallel circuits are easy to design due to their low complexity and are reliable circuits.

Disadvantages of Parallel Circuits

The disadvantages of parallel circuits are:

• Additional Cost: Due to additional components in parallel circuits as compared to series circuits, parallel circuits have an additional cost associated with purchasing components.
• Power Consumption: Due to more components in parallel circuits than series circuits, the power consumption of these circuits can increase drastically. This is common when multiple components are operating simultaneously.
• Complex Diagnosis: In a parallel circuit, Identifying the source of an error can be more difficult as compared to a series circuit because there are multiple paths for current to flow hence multiple sources of error.

Applications of Parallel Circuits

There is a need for Parallel circuits because they have various applications in different fields some of which are given below:-

• Parallel circuits form the major circuit of housing outlets. Since there are different appliances in the household, a parallel circuit ensures each appliance is getting an equal and stable voltage supply.
• Parallel circuits are commonly used in a factory. If someone shuts off a conveyor belt, it’s not going to impact the performance of any other piece of equipment on the factory floor like rollers will still be working. This way we can run the industry in case one equipment fails.
• Security systems also utilize parallel circuits. Earlier security cameras were installed using series circuits but parallel circuits have overpowered them now due to the errors in series circuits. One major issue with a series circuit was that if one part of the circuit fails, the other parts will fail as well resulting in a failed security system. Thereby we use parallel circuits for this.
• Parallel circuits are also used within automobile units, specifically for wiring car headlights. The effectiveness of the other lights is unaffected by a single damaged tail light, ensuring safety.

Solved Example of Parallel Circuits

This example shows how you can mathematical concepts to calculate current and other parameters in a parallel circuit.

Q. Calculate the total current and power across a The voltage2k ohm resistor in the given circuit.

Solved Example

Firstly we calculate the total resistance of the circuit to calculate the current .Let the total resistance be R_eq then 1/R_eq=1/R₁+1/R₂+1/R₃

1/R_eq=1/10+1/2+1/1

R_eq=8/5 k ohms

Now on applying ohms law

V=I*R_eq

9=I*(8/5)

I=45/8 mA

Hence total current in the circuit is 5.625mA

Now we want to calculate power across 2k ohm resistor . Since voltage across each resistor is same we use the formula P=V²/R So Power across 2k= (9)²/2= 40.5 mW

Hence power across 2k resistor is 40.5mV

Difference between Series and Parallel Circuit

The table represents the difference between series and parallel circuits

Parameter	Series Circuit	Parallel Circuit
Voltage distribution	Voltage across each component may not necessarily same	The voltage across each branch is necessarily the same
Current distribution	Current across each component is necessarily the same	Current is divided so current across each component may not be necessarily the same
Overall Resistance	Total Resistance has a larger value than the maximum resistance	Overall Resistance has less value than the minimum resistance
Alignment	In this electrical circuit, components are arranged in a line	In this electrical circuit, components are arranged parallel to each other
Dependency	If one component in the Circuit breaks down, the whole circuit will get damaged.	Other components will function even if one component breaks down since components are independent
Example	An example of a series circuit is a string of Diwali lights. If any one of the bulbs gets damaged, no current will flow and none of the lights will go on.	Parallel circuits are like the smaller veins that divide into branches from our heart and then connect to other parts to return blood to the heart.

Conclusion

We have seen various characteristics of parallel circuits and seen how despite having constant voltage, the current flowing across each component might be different. We know the important laws that govern a parallel circuit. Various real-life insights into parallel circuits have been given for deeper understanding. We have also compared parallel circuits to other types of circuits i.e. series circuits. This has been to understand the importance of both kinds of circuits. Readers can further explore this topic through other gift articles.

FAQs on Parallel Circuits

What is a series circuit?

A series circuit is one in which all circuit elements are arranged in a single path and are connected end-to-end.

What is a parallel circuit?

A circuit is called parallel if the electric current has several paths to pass through. Paths are branches that share a common start and end node.

What is the relation between the total voltage V and the voltage of individual components in a parallel circuit?

The voltage across each component in a parallel circuit is same as total voltage hence V=V₁=V₂=V₃=………..V_N