Kirchhoff's Junction Rule & the Law of Charge Conservation

Instructor: Betsy Chesnutt

Betsy teaches college physics, biology, and engineering and has a Ph.D. in Biomedical Engineering

Kirchhoff's junction rule tells you how current will be distributed when several branches of a circuit meet. In this lesson, learn about the junction rule and how to apply it.

Charge Conservation and Current

Imagine that you have a light bulb. You connect the bulb to a battery and the bulb lights up! What is going on? If you could make yourself really tiny and look inside the wires connecting the bulb and battery, you would see lots of tiny electrons moving around. The battery gives the electrons enough extra energy to push them through the filament of the light bulb. As they go through the filament, they slow down a little and some of their energy is transformed into light!

Does this mean that electrons are disappearing inside the bulb? Do fewer electrons come out than go in? No, the same electrons come out that went in. The only thing that has changed is that they have given up a little bit of their energy. This happens because electrons are charged and the total amount of charge is always conserved. If there is nowhere else for the electrons to go, they MUST come out the other side of the bulb!

The principle of charge conservation means that electrons are not used up by the bulb
light bulb circuit

The flow of electrons through the wires of an electric circuit is known as current, which is measured in units of Amperes (A). Because charge is always conserved, you can determine exactly how current must flow in each branch of a circuit.

Kirchhoff's Junction Rule

In a circuit, sometimes you have places, called junctions, where several wires come together. Because charge is conserved and current measures the rate at which charges are flowing, the total current coming into to a junction must equal the total current coming out the other side of the junction, just as it did in the light bulb. This relationship is known as Kirchhoff's Junction Rule.

The junction rule says that the current going into a junction must equal the current coming out of the junction
junction rule

Applying the Junction Rule to Parallel Circuits

Let's look at how the junction rule can be applied to some real circuits. In this circuit, three branches of the circuit come together at the junction on the left. If 3 A of current flow into the circuit, and 2 A flow out through one of the branches, how much current must be flowing through the third branch?

circuit loop rule example 1

Kirchhoff's Junction Rule tells you that the total current coming into the junction must equal the total current coming out, so the current in the third branch of the circuit must be 1 A.

circuit loop rule example 1 calculations

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