Determining Missing Values & Direction of Electric Current

Instructor: Betsy Chesnutt

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

In an electric circuit, electrons move through the wires, creating currents. If you know the currents in some parts of a circuit but not others, you can use the junction rule to find these unknown currents. Learn how to do just that!

The Junction Rule in Circuits Without Capacitors

At an intersection, a busy highway splits into two new roads. If five cars approach the intersection and two of them take the road to the left, then how many cars must have taken the road to the right? Of course, the answer is three! If five cars went into the intersection, then five cars must have come back out, right?

Just like cars traveling on the highway, inside every electric circuit, there are billions of tiny electrons moving through the wires. Each electron carries a tiny amount of charge, and the flow of this charge is what we call electric current. Electric current is measured in units of Amperes, which is more commonly called Amps (abbreviated A).

Sometimes, there are places in the circuit where several wires come together. We call these places junctions. At a junction, some wires may be carrying current into the junction while others carry current away from the junction, just like different roads may carry cars into and away from an intersection.

Just like the total number of cars on the highway didn't change, in circuits with only resistors and no capacitors, the total amount of charge moving through the circuit doesn't change either! Remember that the charges that create currents are carried by tiny electrons. Electrons do not suddenly pop in or out of existence somewhere in the circuit, so the number of electrons that go into the junction must equal the number coming out of the junction, just as the number of cars going into the intersection had to be equal to the number leaving it. This means that the total current carried into the junction is always equal to the total current coming out of the junction.

This relationship between the current going into and out of a junction is known as Kirchhoff's Junction Rule, and it is one of the fundamental principles governing the behavior of all electric circuits.

Using the Junction Rule

The junction rule is really useful because it allows you to determine the current in different parts of a circuit. For example, look at the circuit below and see if you can determine the missing current.

Did you notice that both I1 and I2 are directed INTO a junction? Since the current going into the junction must equal the current coming out, the missing current, which we can call I3 must be directed OUT OF the junction.

Applying the junction law to this junction gives you the following equation:

I1 + I2 = I3.

Therefore, I3 = 4 A + 2 A = 6 A.

The junction rule still works even when there are more than three currents involved. Remember that all the current going into the junction must equal all the current going out of the junction, no matter how many currents you have.

Can you find the current through the battery shown in the circuit below?

Wow! This circuit is a lot more complicated, right? Even though there are a lot more resistors and batteries here, you can still use the junction law to find this unknown current. If you look closely, you can see that there are three important junctions in this circuit. Let's call them Junction 1, Junction 2, and Junction 3.

Applying the junction rule to Junction 1 allows you to determine that I5 = I1 + I2. Similarly, you can apply the junction rule to Junction 2 to find that I6 = I3 + I4.

Then, you can apply the junction rule to Junction 3 to find that the current through the battery, which we will call I7, is 4 A and is directed to the left.

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