Scott has a Ph.D. in electrical engineering and has taught a variety of college-level engineering, math and science courses.
In this lesson, learn more about parallel electrical circuits. We'll review some electrical circuit fundamentals, look at the defining characteristics of parallel circuits, and explore several concrete examples.
Intro to Electrical Circuits
Most power outlets in U.S. households provide electricity at between 110V and 120V. How is it that all these outlets can maintain the same voltage, even though there may be a number of appliances and components connected to them, all with different power consumptions? In your car, nearly every component that requires electricity (headlights, interior lights, radio, windshield wipers, etc.) runs on a constant 12 volts. How is this possible?
The answer lies in how the electrical circuits are wired. For these and many other electrical systems, the solution is to connect the circuit components in parallel.
What is a Parallel Circuit?
Before we get into a definition of a parallel circuit, let's do a quick review of some electrical circuit fundamentals, mainly voltage, current, resistance, and a few laws. Here are the ones that we'll need:
Voltage (V, in volts - V) is the electrical force responsible for making electrical charge move.
Current (I, in amperes - A) is a measure of the movement of electrical charge over time.
Resistance (R, in ohms) is a measure of how much a component opposes the movement of the current through it.
Kirchoff's Current Law (KCL) is simply an affirmation that charge must be conserved, and so the sum of the currents going into a circuit node (a point in the circuit where two or more components are connected) must equal the sum of the currents going out of the same node:
Kirchoff's Voltage Law (KVL) says that if you sum the voltages around any loop in a circuit, you will get zero:
Applying the Definition: Example
Let's start by looking at a technical definition of a parallel circuit. Two or more electrical components are said to be in parallel if the total electrical current flowing into the parallel network divides among the components then recombines to the same total current afterward. Now this may not seem to be the most intuitive definition, so look at the implications. A parallel circuit will have the following defining characteristics:
It starts with two or more components connected together in a circuit
Each of the components must have only two electrical contacts (wires, conduction paths, etc.)
The components are connected in such a way that they all share the same node on each side of the component
The voltage across all the components connected in parallel is the same
The current flowing into the parallel connection is the same as the current flowing out and is equal to the sum of the individual currents flowing through each component
Let's picture this practical definition as follows:
Electrical components connected in parallel
The voltage across all three components (V) is the same and the KCL equation for either node (top or bottom) is the same, thus all three components are in parallel:
Applying the Definition - Another Example
When trying to decide whether several circuit elements are in parallel, you can't just look at how the circuit is drawn; you must use the electrical characteristics of a parallel circuit. Here is an example:
Circuit with some components not connected in parallel
Which components form a parallel circuit? Only components #1 and #2, because both of them meet the following three conditions:
They share the same nodes at each of their connection points
They each have exactly the same voltage (V) across them
The current flowing into the two components separates into I1 and I2 and then recombines afterward
We cannot say that either component #3 or component #4 is in parallel with #1 and #2 because they don't share the same nodes on each side and the individual voltages across these components must have values that are less than V. We can show this by using the KVL equation for the loop that contains components #2, #3 and #4. Let V3 and V4 be the voltages across components #3 and #4, respectively. Then:
If V3 and V4 are not zero (exceptions are given in the next section) then they must be less than V.
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So what about the use of switches, fuses and circuit breakers in circuits? Are they in parallel? If not, then do we violate the principle of a parallel circuit for the rest of the components? Take a look at the following diagram, which is a simple model for some electrical components in an automobile:
Simplified diagram of automobile electrical components
The components (like lights, radio, wipers, etc.) are shown as R1, R2 and R3. You can see the 12V car battery on the left. This particular circuit also contains three fuses and two switches. For all intents and purposes, we can say that when the switches are closed, their internal resistance is approximately zero and thus they look like wires. Likewise, fuses and circuit breakers, when operating properly, have essentially zero resistance so they too look like a short circuit. Thus, with the fuses operating properly and the switches closed, the circuit now looks like this:
Simplified diagram of automobile electrical components
We can now see that this is indeed a parallel circuit.
Another Example - Batteries in Parallel
Most of the time, when you put batteries into a device, you are connecting them in series. The reason you do this is because the voltages add up when batteries are connected in series. For example, you might be inserting four 1.5V AA batteries into a device that operates at 6V. What happens if you connect batteries in parallel? Well, first you should make sure they are the same voltage. Why? Because, as we have seen, the voltage across parallel connected components must be the same. Damaging things can happen if you connect two batteries of different voltages in parallel. Connecting multiple batteries of the same voltage in parallel simply increases the amount of total current you can deliver to the circuit before the batteries run out of charge.
Here's a concrete application. Suppose you own a trailer and the electrical systems run on a rechargeable 12V automobile battery. You observe that you can go camping without charging the battery for 3 days. What if you would like to make that 6 days? If you connect a second 12V battery in parallel with the first, then each battery will only have to deliver half the current that the single battery needed to. Since current is the movement of charge, you have doubled the amount of charge available for camping! Here's a simplified picture:
12V parallel circuit used to double battery life
A parallel circuit is one that has the following characteristics: 1) it involves two or more components that each have exactly two contacts each; 2) the components share the same nodes on either side; 3) all components in parallel have the same voltage across them; and 4) current divides going through the components and then recombines on the other side to the same total current. Circuits are shown to be parallel electrically using Kirchoff's Current Law (KCL) and Kirchoff's Voltage Law (KVL), not by how the circuit is drawn. Batteries connected in parallel should have the same source voltage; battery life is multiplied by the number of batteries in parallel.
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