Why Do You Need To Know About KVL?You are at: Basic Concepts - Kirchoff's Laws - KVLUsing KVL To Write Equations For CircuitsWhat If?Problems
Kirchhoff's Voltage Law - KVL - is one of two fundamental laws in electrical engineering, the other being Kirchhoff's Current Law (KCL).
What should you be able to do after this lesson? Here's the basic objective.
Given an electrical circuit:These goals are very important. If you can't write KVL equations and solve them, you may well be lost when you take a course in electronics in a few years. It will be much harder to learn that later, so be sure to learn it well now. (And, if you need to review the concept of voltage, here is a link to that lesson.Be able to write KVL for every loop in the circuit.
Be able to solve the KVL equations, especially for simple circuits.
Here's a simple circuit. It has three components - a battery and two other components. Each of the three components will have a current going through it and a voltage across it. Here we want to focus on the voltage across each element, and how those three voltages are related.
Here's the same circuit. Here, with the button, you can move the dot representing charge around the circuit.
Q1. As the charge moves from the top of the battery to the top of Element #1 (along the wire shown in purple), how much energy does the charge lose?
Q2. As the charge moves from the top of Element #1 through Element #1 to the bottom of element #1, how much energy does the charge lose?
Q3. As the charge moves from the bottom of Element #1 to the top of Element #2, how much energy does the charge lose?
Q4. As the charge moves from the top of Element #2 through Element #2 to the bottom of element #2, how much energy does the charge lose?
Q5. As the charge moves from the bottom of Element #2 to the bottom of the battery, how much energy does the charge lose?
Q6. As the charge moves from the bottom of the battery through the battery to the top of the battery, how much energy does the charge lose?
There is a good algorithm that can be stated for how to write the KVL equations for a loop. We'll need that when we examine this circuit again. Here's the statement of the algorithm.
Before we write the KVL equations, we need to notice something. The answer to Question #7 may not be correct. Let's think a little deeper to be sure we have it right. We took the correct answer to be two loops. In a sense that's correct, but in another sense there are three loops. In the picture below, each of the three buttons - when pressed - will show you one of the three loops. There's a loop there that you might not have thought about. Click the three buttons to see the three loops.
Actually, that's not right, because we do not get three independent equations. There are only two independent equations we can write.
That's not immediately obvious, so write the three equations as shown below. We'll put a horizontal line between the first two and the third equation.
-V_{B}
+ V_{1} + V_{2} = 0
-V_{2}
- V_{3} + V_{4} = 0
Can you see that you can add the first two equations to get the third? (Actually, there is a -V_{2} and a +V_{2}, and those are the only things that cancel out when you add.) The third equation can be obtained from the first two equations, so it is not an independent equation. When you have the first two equations you can get the third from them!
What this means is that you have to be careful when you write KVL. You can write too many equations, and in being careful you might not write enough. Fortunately, if you look at a circuit you can almost always see how many independent loops there are by inspection. Going back to our question about how many loops there are in this circuit, the answer is that there are three loops but only two independent loops.
Now, let's see if you can apply your knowledge of KVL to solve a few simple
problems.
P1. Using
the same circuit you have been examining, answer the following questions.
For the first problem if the battery is a 9v battery, and you know that
V_{1} = 3.7v, what is the value of V_{2}
(in volts)?
P2. You
also know that V_{4} = 1.3v. What is the value of
V_{3} (in volts)?
P3. Now,
you have the voltages across all of the elements and the battery.
Check your knowledge of KVL by putting your numbers into each of the three
loop (KVL) equations for the circuit.
P4. Consider
the case of two flashlight batteries. Inside a flashlight they are
usually stacked something like the way they are shown below. There
is also a voltmeter shown. It is connected to measure the voltage
of the two batteries in series. Draw an equivalent circuit diagram
that can be used to represent this situation. Compute the voltage
that is measured by the voltmeter using KVL if each battery has 1.54v.
P5. Here is a circuit. Determine all of the loops in this circuit and write KVL for every loop.
P6. Here is a circuit. The voltage across element 1 is V1, etc. Write the KVL equations for the following loops:
KVL gives a lot of information about a circuit. However, it doesn't give you everything you need to know all of the time. Sometimes you will need information from KCL - Kirchhoff's Current Law. You will also, always need the information that is contained in the descriptions of the elements themselves. For example, resistors have a relationship between the current flowing through the resistor and the voltage across the resistor. That information is crucial if there's a resistor in a circuit.
Still, without KVL you won't get very far analyzing circuits, so you will
definitely use the information and concepts you learned in this lesson.