Electron educators

Course Content
Kirchhoff’s current law
The holy grail of network theory is right here, so lets get started into the world of electronics.
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Kirchhoff’s current law
KCL quiz
Lab KCL
Kirchhoff’s voltage law
This is a very nice follow up to see what other work Kirchhoff did to help you solve electric networks.
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Kirchhoff’s voltage law
KVL quiz
Ohm’s law
Most of you will have learned this in high school. I think this is the most known formula in electronics, and we cover it here.
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Ohm’s law
Ohm's quiz
Node voltage analysis
This is where is real hard work start. Node voltage analysis allows us to use KCL to solve complex circuits.
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Node voltage
Node voltage quiz 1
Voltage and current sources
Node voltage quiz
Mesh current analysis
So we solved complex circuits with KCL and node voltage analysis. We can do the same with KVL only this time it is called the mesh current analysis.
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Mesh current analysis
Mesh current quiz
Super position
Not one but two, three, four, a thousand sources in your circuit. No problem, we can solve this with superposition (although a thousand is still a lot of work).
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Superposition principle
Superposition quiz
Thévenin equivalence
Thévenin is all about simplifying circuits. We can use this to reduce parts of circuits to a single voltage source with a resistor.
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Thévenin transformations
Norton equivalence
No only Thévenin has an equivalence circuit, so does Norton.
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Norton transformations
Dependent sources
You can hate these, but you'll get to love these, the dependent sources. They are our vital building blocks for the most awesome electronic component, the mighty transistor! This is also the final part we will master during this course.
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Dependent sources
Network theory

Kirchhoff’s Voltage Law

Mr Kirchhoff did more work besides his current law. He also devised a voltage law, besides his current law (he might have had a little too much time on hands). This law is called Kirchhoff’s Voltage Law (KVL) and it states:

If you go around any closed loop in a circuit, all the voltages you encounter sum up to zero.

Or mathematically:

\(V_0 + V_1 + \ldots + V_n = 0 \)

Looks a lot like our KCL equation doesn’t it?

Now this might sound a bit confusing, the voltages in a loop. So lets look at an example.

Figure 1. Kirchhoff’s Voltage Law (KVL)


As can be seen we have four voltages \(V_1 \), \(V_2 \), \(V_3 \), and \(V_4 \).
If we were to add all the voltages in a loop together we should get 0 volts according to Kirchhoff. Lets go around the loop clockwise and see if it is true.

  1. We start at \(V_1 \) and we enter the component at the ‘-‘ terminal, because if we follow the arrow around the circuit (clockwise), we will first encounter the ‘-‘ terminal. So our formula becomes: \(-V_1 = 0 \).
  2. Next up is \(V_2 \), which we enter through the ‘+’ terminal. We add this to the equation: \(-V_1 + V_2 = 0 \).
  3. Following the loop we encounter \(V_3 \), giving us: \(-V_1 + V_2 + V_3 = 0 \).
  4. And last but not least, we find \(V_4 \), which is also added to our equation to get: \(-V_1 + V_2 + V_3 + V_4 = 0 \).

Now if we fill in all the numbers we get: \(-9 + 4 + 2 + 3 = 0 \) \(-9 + 9 = 0 \)

This seems to be valid. Now you might be wondering if I just picked these numbers to they would add up nicely, and yes I did, but in a real circuit this is also true, quite neat!

Example with 2 loops

KVL also works in a more complicated circuit.

Figure 2. Two loops

In the circuit above we have two loops. \(V_2\) and \(V_5 \) are unknown. For the rest of the voltages we take: \(V_1 = 10V \), \(V_3 = 2V \), \(V_4 = 1V \), \(V_6 = 1V \) and \(V_7 = 5V \).

We have two loops in this circuit and lets see if we can solve them.

Going around Loop 1 gives us:
\(-V_1 + V_2 + V_7 + V_6 = 0 \)
\(-10 + V_2 + 5 + 1 = 0 \)
\(-4 + V_2 = 0 \)
\(V_2 = 4V \)

Solving Loop 2 gives us:
\(-V_7 + V_3 + V_4 + V_5 = 0 \)
\(-5 + 2 + 1 + V_5 = 0 \)
\(-2 + V_5 = 0 \)
\(V_5 = 2V \)

Now we can check if KVL is really valid. Because it states any loop should be valid. So lets check this by taking the outer loop consisting of : \(V_1 \), \(V_2 \), \(V_3 \), \(V_4 \), \(V_5 \) and \(V_6 \).
If we add them all up we should get:
\(-V_1 + V_2 + V_3 + V_4 + V_5 + V_6 = 0 \)
\(-10 + 4 + 2 + 1 + 2 + 1 = 0 \)
\(-10 + 10 = 0 \)
It is always so satisfying when it all matches up.

The flaw of KVL

There is one downside of KVL. KVL can only be used if a schematic is planar. That is a fancy word of saying it can be draw without any crossing lines. Fortunately, most circuits are planar. More complex circuits can be non-planar. See the example below:

Figure 3. Non-planar circuit

If we try to place a resistor from point A to point B we cannot do this without crossing a line. In this case KVL will not be valid, as we have to cross at least one line. In all other cases it is. It is not perfect, but very useful as we will see later on. And that all you need to know about KVL at this moment, so off to the exercises.

 

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