Study Material

Parallel circuit

We explain what a parallel circuit is, its characteristics, how to do it and we give several examples. define parallel circuit

define parallel circuit
Two bulbs connected in parallel, powered by a direct voltage source (left) and provided with a switch (at the bottom) to control the passage of current

The parallel circuit is one whose elements are connected through two points in common. In this way, the receiving component is subject to the same voltage and acts independently of the other elements. define parallel circuit

The following figure shows two small lights connected in this way. The current leaves the positive pole of the battery, and when it reaches the bulbs it divides, turning them on.

Then the currents coming out of the bulbs join again and return to the negative pole to start the cycle again. A switch is also seen in the circuit, which is used to turn the circuit on and off at will.

There is an obvious advantage to parallel connection: if one of the bulbs burns out, the other is still on. This is because the current needs a closed path to flow. If a light bulb burns out, that part of the circuit is left open and current cannot flow through it, but it still has the path of the other light bulb. define parallel circuit

Characteristics of parallel circuits

The elements that receive the current and make use of it, called receptors , are at the same voltage as the source or generator.

The current from the source is divided in each of the receivers of the circuit and they are added in such a way that, at the end of the tour, the original current returns to the source. define parallel circuit

-It is considered that the conductors that join the elements of the circuit lack resistance, however, in practice, the cables do offer a small resistance to current, which in some cases produces significant effects. define parallel circuit

-Each element of the circuit works independently of the others. Since the current has multiple paths to circulate, if any of the components fails, the current does not pass through the damaged element, but is redistributed in the others.

-Adding resistors in parallel does not increase the total or equivalent resistance of the circuit. In fact, the equivalent resistance in parallel is less than any of the individual component resistors. define parallel circuit

The points of the circuit where the current is divided, or several currents converge, are called nodes . In the circuit shown above there are two nodes: the one on the left, where the current coming from the battery is divided, and the one on the right, where the currents coming out of each bulb meet again.

-Each closed portion of the circuit corresponds to a mesh .

Components in parallel define parallel circuit

It is possible to replace a set of elements connected in parallel, by a single component of the same class, called an equivalent. The following figure illustrates the symbols used and the resulting configuration: define parallel circuit

define parallel circuit: Components in parallel
Resistors, inductors, capacitors and batteries connected in parallel.

The formulas to determine the different equivalents are given below: define parallel circuit

Resistors in parallel define parallel circuit

The equivalent resistance of n resistors in parallel is calculated through:

Resistors in parallel

Inductors in parallel

The equivalent inductance of n parallel inductors is calculated in a similar way to resistors, with the formula:define parallel circuit

Inductors in parallel

Capacitors in parallel

The equivalent capacitance of n capacitors placed in parallel is the sum of the capacities of each one:


Batteries in parallel define parallel circuit

The voltage of a configuration of identical batteries in parallel is the same of one of them.

How to make a circuit in parallel?

A parallel circuit with 3 resistors is easily assembled with the following materials: define parallel circuit

  • A proto board or tablet to support circuits.
  • 3 commercial resistors.
  • Connection cables.
  • Multimeter.
  • Switch.
  • Battery or battery.

Process define parallel circuit

The support board has holes to insert the terminals of each element. Beneath the board are thin copper lines connecting the dots. The assembly is as shown in the figure:

define parallel circuit: Circuit of 3 resistors in parallel
Circuit of 3 resistors in parallel.

With the multimeter you can measure the equivalent resistance (the measurement is made by disconnecting the power supply), and also the voltage and current through each element.

Examples of parallel circuits

Measurement of voltages

It is carried out with a voltmeter, which is built into a multimeter. The multimeter is used to measure the most common electrical quantities, usually current, voltage, and resistance. define parallel circuit

To measure the direct voltage or the effective value of the alternating voltage, the voltmeter tips are placed in parallel with the element to be measured. define parallel circuit

The resistive current divider

It is made with two or more resistors in parallel, fed with a direct or alternate source.

The following figure shows a current divider with two resistors R 1 and R 2  supplied with an ideal voltage source ε. It is precisely the circuit diagram shown at the beginning of the article, where the bulbs are the resistors and the switch is denoted by the letter S: define parallel circuit

The resistive current divider
Current divider with two resistors.

The current I that leaves the battery is divided when it reaches the node, which is the green point. By the resistance R 1 passes current I 1 and the resistance R 2 , flows the current I 2 . Upon reaching the yellow node, both currents join again to form I and continue the cycle.

1 + I 2 = I

By means of Ohm’s law it is shown that the currents I 1 and I 2 are: define parallel circuit


Batteries connected in parallel

Batteries or cells can be connected in parallel as long as they are of the same voltage, thus increasing the capacity of the assembly, a measure of how much charge passes through the terminals after one hour when a current of 1 A.

A battery with a capacity of 10 Ah (Amp-hour) supplies 10 amps in 1 hour, or 1 amp in 10 hours. As 1 Ah equals 3600 C, this means that the battery has a capacity of 36000 C.

The capacity of the parallel connection is the sum of the individual capacities, very useful for connecting more devices. But it must be taken into account that in practice the life of batteries is shortened, because they have different internal resistances, even if they are identical and come from the same manufacturer.

The wiring, on the other hand, also has resistance, which causes current imbalances, so that almost always one of the batteries ends up going through more charge and discharge cycles than the other and deteriorates first. define parallel circuit

Domestic electricity system

Parallel circuits are essential in the electrical system of buildings, since their main characteristic is that the circuit continues to function, even if a component is damaged.

When a light bulb burns out, for example, the corresponding part of the circuit remains open and no current flows through it. If the appliances were connected in series with the burned out light bulb, they would stop working. Furthermore, the parallel connection of several resistors does not limit the total current supplied by the source. define parallel circuit

Car light system

The car’s light system also consists of circuits in parallel, for the reason explained above: if one headlight stops working, the rest of the system is still shining. define parallel circuit

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