Kirchhoff Laws

Edoardo Sorgentone

http://www.edoardosorgentone.it/

After you read this tutorial, you will learn how to solve a circuit with Kirchhoff Laws so that you will know the behavior of a electrical circuit and its fundamental quantities. Kirchhoff Laws are used in electrotechnics to solve circuits.

Solving a circuit is essential: it means that you know value of voltage and current of each component.

In the last article I talked about electronic theory basics.Now we will see a more practical topic.

ARGUMENTS:

• Kirchhoff Laws: KCL,KVL,how to solve a circuit

• Tellegen Theorem

• Series and parallel connection

• Exercises

• Voltage and Current Divider

1-Kirchhoff Laws

KIRCHHOFF CURRENT LAW(KCL)

KCL is the Kirchhoff first law and it express the conservation of charge entering and leaving a node.

The same goes for any closed surface.

CONVENTION: it is considered positive a current that leave the node and negative a current that enters in the node.

This is what the example circuit would look like:

KIRCHHOFF VOLTAGE LAW(KVL)

KVL is the same of KCL but for voltage in a loop:

convention: counterclockwise turn on the loop; when you first meet the + and then the -, that voltage on that component will be positive.Let’s see an example:

So here v1 will be positive since you meet + first.

v2 is negative because you meet first - and then +(when turning counterclockwise).

v3 is positive because you meet + first.

Sometimes you have to assign signs: if you have the current sign, you have to assign the voltage, just assign + on the terminal in which current enter and - to the terminal in which current exit.

TELLEGEN THEOREM

SERIES AND PARALLEL CONNECTION

When connecting 2 elements, really often they can be connected in 2 ways:series or parallel.

In some cases components are neither in series nor in parallel(in that case you have to use Y-∆ connection), but let’s take it slow and learn first series/parallel.

The great thing is that you can transform series and parallel connected resistors into a single equivalent resistor.

Series:

Parallel:

Another formula that can be used for parallel is this: 1

Now let’s see some exercises:

In the first exercise, resistors are all in parallel, so you solve it calculating the equivalent 2 by 2.

In e.2 resistors are just in series so it is really simple to solve it.

VOLTAGE AND CURRENT DIVIDER

A voltage divider is a simple circuit that consists of two resistors connected in series across a voltage source. It divides the total voltage across the resistors in proportion to their resistance values.

$$voltage \space divider:v_1=v_{s}\frac{R_1}{R_1+R_2}$$

A current divider is a similar concept but is used to divide the current flowing through a branch of a parallel circuit into different currents. It involves two or more parallel resistors through which the current is split in proportion to their resistances.

$$current \space divider:i_1=i_s\frac{R_2}{R_1+R_2}$$

Now it’s your turn!

Practice as much as possible with Kirchhoff Laws, I’ll give you an exercises:

ps:use Kirchhoff Laws.

Feel free to send me an email if something is not clear! 😄

Edoardo Sorgentone

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http://www.edoardosorgentone.it/services.html