Kirchhoff's Law: Definition & Application

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  • 0:02 Current and Voltage
  • 1:28 Kirchhoff's Laws
  • 2:14 An Example Problem
  • 5:27 Lesson Summary
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Lesson Transcript
Instructor: Betsy Chesnutt

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

Kirchhoff's laws can be used to analyze complex circuits. In this lesson, you will learn about Kirchhoff's two laws and how to apply them to circuit analysis.

Current and Voltage

When you flip on the light switch, the light comes on immediately, right? Why does this happen? What is going on inside the wires in your walls and in the light bulb to make the bulb light up?

If you could make yourself really small and look inside the wires connecting the light switch and the bulb, you would see that when you flip the switch, billions of tiny electrons start moving through the wires of this electric circuit and their energy is what makes the bulb light up.

There are two important concepts that you must understand to know how an electric circuit works:

  1. Current is the flow of electrons around the circuit. In order for current to flow, the wires of the circuit must make a complete circle. If there's a break anywhere, the electrons will not have any way to get across the gap and current will stop. This is why the light doesn't come on until you flip the switch. The switch closes a gap in the circuit and allows current to flow.
  2. Voltage is the difference in electric potential between two points in the circuit. Certain circuit elements, like batteries, are voltage sources and provide energy to the electrons so that they will move around the circuit. Other elements, like the light bulb, are resistors that take the energy provided by the battery and transform it into other forms of energy, like light. Because of this, the voltage across a resistor will be negative.

Kirchoff's Laws

Named for their creator, Gustav Kirchhoff, Kirchhoff's laws can help you to understand current and voltage in a circuit and can also be used to analyze complex circuits that can't be reduced to one equivalent resistance using what you already know about series and parallel resistors.

Kirchhoff's junction law says that the sum of currents entering a junction must equal the sum of currents leaving the junction. Current is never used up in a circuit, so it makes sense that all the current that goes into the junction must come back out, too.

Kirchhoff's loop law says that the sum of the changes in voltage around and closed loop in a circuit must always be zero. This means that if you add up the voltage across each circuit element all the way around the loop, you would get zero.

An Example Problem

Let's look at how to use Kirchhoff's two laws to analyze a complex circuit like the one on your screen right now:

circuit example

resistance and voltage values

The first step is to determine how many branches there are in the circuit and define a current variable for each branch. You need to find only one current in each branch, because every point in a branch will have exactly the same amount of current; but different branches may have different currents.

circuit with labeled currents

In this circuit, you can see that we have three branches, and we have labeled the three currents and defined their direction. Now, how did we know the direction of the current in each branch? We didn't! Most of the time in a complex circuit like this, you will not be able to tell which direction current will flow in a branch of the circuit just by looking at it.

That's okay! You just need to pick a direction and make sure that all your calculations are consistent with it. If you picked the wrong direction, when you calculate the current, it will be negative. This will let you know that the current is actually going in the opposite direction from the way you predicted.

You can now use the junction law to write the first equation that we will use to analyze this circuit.

junction rule equation

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