Parallel circuits

09/04/2026

The online parallel circuit simulations on this page allow you to interactively understand how current, voltage, and equivalent resistance behave in a simple circuit. Through virtual setups with a power source, switch, bulbs, resistors, ammeters, and voltmeters, you can check the relationship between the circuit current, resistance values, and voltage drops at different points.

What are parallel electric circuits

Parallel circuits are characterised by their components being connected in such a way that they form multiple branches, each with its own path for current. In this type of setup, the voltage across each branch is the same, whilst the total current from the source is divided among the different branches according to the value of their resistances. The equivalent resistance is obtained by summing the reciprocals of each connected resistance. Parallel circuits are a basic and straightforward configuration that forms the foundation for analysing more complex arrangements.

Formula for equivalent resistance

When several resistors are connected in parallel, their combined effect on the circuit can also be expressed as a single equivalent resistance. In this case, the equivalent resistance is found by summing the reciprocals of each connected resistance, using the following formula:

1/R_eq = 1/R₁ + 1/R₂ + 1/R₃ +…+ 1/R_n

The voltage applied to each branch is the same, whilst the total circuit current is shared among the different branches according to their respective resistance values. In this way, the equivalent resistance represents the total opposition to the flow of current in a circuit with multiple available paths.

Practical example

Suppose we have three resistors connected in parallel with values of 10 Ω, 20 Ω, and 30 Ω. The equivalent resistance of the circuit is found by adding the reciprocals of each resistance:

1/R_eq = 1/10 + 1/20 + 1/30 = 0,100 + 0,050 + 0,033 = 0,183

R_eq = 1/0,183 = 5,46 Ω

This means that, from the perspective of the power supply, the set of resistors behaves as a single resistance of approximately 5.46 Ω. The voltage applied to each branch is the same, whilst the total current supplied by the source is divided among the three resistors according to their values. For example, if the source provides 12 V, the currents will be 1.2 A through the 10 Ω resistor, 0.6 A through the 20 Ω resistor, and 0.4 A through the 30 Ω resistor, which adds up to a total of 2.2 A.

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Parallel circuit simulations

Voltage
Current
Equivalent
Branches

Constant voltage

In this simulation, a circuit is built with a source, a switch, and a bulb and a resistor connected in parallel. A voltmeter is placed in each branch of the circuit to check that the voltage is the same in all of them and that it also matches the battery voltage. Change the resistance values and the battery voltage to verify that this property always holds in parallel connections.

Current distribution in parallel circuits

In this simulation, a circuit is built with a source, a switch, a bulb, and several resistors connected in parallel. A voltmeter is placed across the ends of the resistors. Additionally, ammeters are used in each branch and at the output of the source. Observe how the total current supplied by the battery is shared among the resistors in proportion to their value and how the sum of the partial currents matches the total current supplied by the source. Change the resistance values and the battery voltage to verify that this rule always holds.

Equivalent resistance in a parallel circuit

In this simulation, a circuit is constructed with a source, a switch, a bulb, and several resistors connected in parallel. A voltmeter is placed across the ends of the resistors and an ammeter to measure the total current supplied by the source. Calculate the equivalent resistance by measuring the total current and applying Ohm’s law (Req = V/I). Verify that the value obtained matches the result of adding the reciprocals of the individual resistances. Modify the resistance values and battery voltage to check that the rule always holds.

Branch independence

In this simulation, a circuit is built with a source, a main switch, and two branches connected in parallel: one with a bulb and another with a resistor. Each branch has its own switch. Observe how, when opening or closing any of the branch switches, the other continues to operate normally. The voltage in each branch remains constant, and only the total current supplied by the source changes. Change the resistance values and battery voltage to see how the total current varies without affecting the independent operation of each branch.

Giants of science

“If I have seen further, it is by standing on the shoulders of giants”

Isaac Newton

André-Marie Ampère

1775

–

1836

André-Marie Ampère formulated the theory of electromagnetism, establishing the mathematical foundations linking electricity and magnetism

“Science is the explanation of the complex by the simple”

James Clerk Maxwell

1831

–

1879

James Clerk Maxwell formulated Maxwell’s equations, unifying electricity and magnetism and predicting electromagnetic waves

“Thoroughly conscious ignorance is the prelude to every real advance in science”

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“If I have seen further, it is by standing on the shoulders of giants”

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1775

–

1836

André-Marie Ampère formulated the theory of electromagnetism, establishing the mathematical foundations linking electricity and magnetism

“Science is the explanation of the complex by the simple”

Michael Faraday

1791

–

1867

Michael Faraday discovered electromagnetic induction, conducted pioneering experiments in optics (Faraday effect), and established fundamental principles of electrochemistry.

“Nothing is too wonderful to be true”

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Your path to becoming a giant of knowledge begins with these top free courses

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Principles of Modeling, Simulations, and Control for Electric Energy Systems

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Test your knowledge

What is a parallel circuit?

A parallel circuit is an electrical circuit in which components are connected across several branches, each providing its own independent path for the current. This means the current does not pass through all components one after another; instead, it splits among the available branches. In this configuration, every component receives the same voltage, regardless of how many branches there are or what their resistances are. One major advantage of parallel circuits is that if one component stops working, the others continue operating normally because each branch is independent. For this reason, parallel circuits are used in most household electrical installations and in systems where each device must function on its own.

How do current and voltage behave in a parallel circuit?

In a parallel circuit, the voltage is the same across all branches because each one is directly connected to the source. The current, however, divides among the branches depending on their resistance: branches with lower resistance receive more current, while those with higher resistance receive less. The total current supplied by the source is the sum of the currents flowing through each branch. This behavior allows each component to operate independently, since all of them receive the same energy per unit charge even though the amount of current flowing through each branch may differ.

Why do other components keep working if one fails in a parallel circuit?

This happens because each component has its own path for the current. If one branch is interrupted, only that specific path stops conducting, while the remaining branches stay intact and continue receiving energy. It is similar to having several parallel roads: if one is closed, the others remain open and traffic can still flow. This is why parallel circuits are ideal for systems where a single failure should not affect the rest, such as home lighting, where one burnt‑out bulb does not turn off all the others. .

Why do components in parallel not affect each other’s brightness or performance?

In a parallel circuit, every component receives the same voltage, no matter how many are connected. This means a lamp, motor or any device works as if it were connected directly to the source. Adding more branches does not reduce the voltage each component receives. The only thing that changes is the total current the source must supply, not the current flowing through each branch. As long as the source can provide the required current, adding more devices does not make the others perform worse.

Where are parallel circuits used in real life?

Parallel circuits are used in almost all modern electrical systems because they allow each device to operate independently. In a home, every lamp, outlet and appliance is connected in parallel so that a failure in one does not affect the others. They are also used in vehicle lighting systems, electronic devices and any application where each component must receive the same voltage. This configuration provides safety, stability and flexibility, making it the most practical choice for most electrical installations.