How do you use Kirchoff's Laws in electric circuits?

Question

I do not want a link. Explain. :)

Answer 1

Kirchhoff's current law can be used to solve electrical circuit analysis. Basically since the sum of all the currents at one node is equal to zero you are able to make multiple independent equations to solve the unknowns. Just sum up all the currents at one node and equal it to zero and you have an equation.

Answer 2

Kirchhoff's Laws are conservation principals. That is, they must express a balance. Take the current law,

Circuit elements connect at a point, called a node. For example, 3 resistors forming a T. Kirchhoff's current law says "all the current ENTERING the node must sum to zero." Current can only flow into or out of the node. Hence, the current law say not all the current can be flowing into the node. Mathematically it looks like this,

I1 + I2 + I3 = 0 where,

I1 = Current in Resistor 1
I2 = Current in Resistor 2
I3 = Current in Resistor 3

Kirchhoff's Voltage law is the same kind of law, but instead of nodes it applied to loops. That is, starting at a particular node you move around the circuit from one node to the next, until you complete a loop back to the starting node. The law is, the sum of all the voltage-drops must equal zero. A voltage drop is the difference in voltage from one node to the next. A battery represent a voltage gain, and a Resistor is a voltage drop. So, in a loop that include, say, 3 Resistors, and 1 battery, the sum of the voltages drops across the Resistors must equal the gain the Battery represents.

Answer 3

To solve for unknown voltages and currents.

For example, since the law of the conversation of energy states that all voltage drops around a closed loop must add up to zero (Kirchhoff's Voltage Law), then if you have a 10 volt battery (voltage rise) in a loop with an unknown voltage drop across an LED, and a 3 volt voltage drop across a resistor, how many volts is the LED using? 10 + (-3) + x = 0, so 10 - 3 = x volts where x must be 7 volts.

All currents leaving a node must add up to zero (Current Law). If you have ten amps flowing into a node, and five volts flowing out, how much current is flowing out of the other branch? Obviously 10 -5 = 5 amps.

It gets a little more complicated, but you get the idea.

Answer 4

Through experimentation in 1857 the German physicist Gustav Kirchhoff developed methods to solve complex circuits. Kirchhoff developed two conclusions, known today as Kirchhoff’s Laws. Law 1: The sum of the voltage drops around a closed loop is equal to the sum of the voltage sources of that loop (Kirchhoff’s Voltage Law). Law 2: The current arriving at any junction point in a circuit is equal to the current leaving that junction (Kirchhoff’s Current Law). Kirchhoff’s two laws may seem obvious based on what we already know about circuit theory. Even though they may seem very simple, they are powerful tools in solving complex and difficult circuits. Kirchhoff’s laws can be related to conservation of energy and charge if we look at a circuit with
one load and source. Since all of the power provided from the source is consumed by the load, energy and charge are conserved. Since voltage and current can be related to energy and charge, then Kirchhoff’s laws are only restating the laws governing energy and charge conservation. The mathematics involved becomes more difficult as the circuits become more complex. Therefore, the discussion here will be limited to solving only relatively simple circuits.

Kirchhoff’s Voltage Law

Kirchhoff’s first law is also known as his "voltage law." The voltage law gives the relationship between the "voltage drops" around any closed loop in a circuit, and the voltage sources in that loop. The total of these two quantities is always equal. In equation form: Esource = E1 + E2 + E3 + etc. = I1R1 + I2R2 + I3R3 + etc. SEsource = SIR (2-14)
where the symbol S (the Greek letter sigma) means "the sum of."
Kirchhoff’s voltage law can be applied only to closed loops. A closed loop must meet two conditions:
1. It must have one or more voltage sources.
2. It must have a complete path for current flow from any point, around the loop, and back to that point.
You will remember that in a simple series circuit, the sum of the voltage drops around the circuit is equal to the applied voltage. Actually, this is Kirchhoff’s voltage law applied to the simplest
case, that is, where there is only one loop and one voltage source.

Kirchhoff’s Current Law

Kirchhoff’s second law is called his current law and states: "At any junction point in a circuit, the current arriving is equal to the current leaving." Thus, if 15 amperes of current arrives at a
junction that has two paths leading away from it, 15 amperes will divide among the two branches, but a total of 15 amperes must leave the junction. We are already familiar with Kirchhoff’s current law from parallel circuits, that is, the sum of the branch currents is equal to the total current entering the branches, as well as the total current leaving the branches. Normally Kirchhoff’s current law is not used by itself, but with the voltage law, in solving a problem.

Answer 5

Kirchoff's cutting-edge regulation - The sum of each and every of the currents coming right into a junction (financial enterprise of resistors and so on) could desire to equivalent the fairly some the currents leaving that junction. Kirchoff's voltage regulation - The sum of all voltage drops in a closed loop could desire to equivalent 0 desire this helps!

Answer 6

While you don't want a link, I copied it from:http://math.fullerton.edu/mathews/n2003/KirchoffMod.html
I suggest you go to the link.
Module for Kirchoff's Law

Background

Solution of linear systems can be applied to resistor network circuits. Kirchoff's voltage law says that the sum of the voltage drops around any closed loop in the network must equal zero. A closed loop has the obvious definition: starting at a node, trace a path through the circuit that returns you to the original starting node.

Network #1

Consider the network consisting of six resistors and two battery, shown in the figure below.

[Graphics:Images/KirchoffMod_gr_1.gif]

There are two closed loops. When Kirchoff's voltage law is applied, we obtain the following linear system of equations.

[Graphics:Images/KirchoffMod_gr_2.gif]

Proof Kirchoff's Law Kirchoff's Law

Computer Programs Kirchoff's Law Kirchoff's Law

Example 1. Solve the network #1 for the currents [Graphics:Images/KirchoffMod_gr_3.gif] given the following value for the resistors and battery:

[Graphics:Images/KirchoffMod_gr_4.gif].
Solution 1.

Example 2. Solve the network #1 for the currents [Graphics:Images/KirchoffMod_gr_26.gif] given the following value for the resistors and battery:

[Graphics:Images/KirchoffMod_gr_27.gif].
Solution 2.

Network #2

Consider the network consisting of nine resistors and one battery, shown in the figure below.


[Graphics:Images/KirchoffMod_gr_49.gif]

There are three loops. When Kirchoff's voltage law is applied, we obtain the following linear system of equations.

[Graphics:Images/KirchoffMod_gr_50.gif]

Example 3. Solve the network #2 for the currents [Graphics:Images/KirchoffMod_gr_51.gif] given the following value for the resistors and battery:

[Graphics:Images/KirchoffMod_gr_52.gif].
Solution 3.

Example 4. Solve the network #2 for the currents [Graphics:Images/KirchoffMod_gr_79.gif] given the following value for the resistors and battery:

[Graphics:Images/KirchoffMod_gr_80.gif].
Solution 4.

Network #3

Consider the network consisting of six resistors and two batteries, shown in the figure below.


[Graphics:Images/KirchoffMod_gr_107.gif]

There are three loops. When Kirchoff's voltage law is applied, we obtain the following linear system of equations.

[Graphics:Images/KirchoffMod_gr_108.gif]

Example 5. Solve the network #3 for the currents [Graphics:Images/KirchoffMod_gr_109.gif] given the following value for the resistors and batteries:

[Graphics:Images/KirchoffMod_gr_110.gif].
Solution 5.

Example 6. Solve the network #3 for the currents [Graphics:Images/KirchoffMod_gr_137.gif] given the following value for the resistors and batteries:

[Graphics:Images/KirchoffMod_gr_138.gif].
Solution 6.

Research Experience for Undergraduates

Kirchoff's Law Kirchoff's Law Internet hyperlinks to web sites and a bibliography of articles.

Download this Mathematica Notebook Kirchoff's Law

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(c) John H. Mathews 2004

Answer 7

Kirchhoff's Law Conclusion