Adrian R. Managbanag
BSESE 2B
Kirchhoff’s Circuit Law

Kirchhoff's circuit laws are two approximate equalities that deal with the current and voltage in electrical circuits. They were first described in 1845 by Gustav Kirchhoff. This generalized the work of Georg Ohm and preceded the work of Maxwell. Widely used in electrical engineering, they are also called Kirchhoff's rules or simply Kirchhoff's laws (see also Kirchhoff's laws for other meanings of that term).

Both of Kirchhoff's laws can be understood as corollaries of the Maxwell equations in the low-frequency limit -- conventionally called "DC" circuits. They serve as first approximations for AC circuits.

Kirchhoff’s Current Law

This law is also called Kirchhoff's first law, Kirchhoff's point rule, or Kirchhoff's junction rule (or nodal rule).

The principle of conservation of electric charge implies that:

At any node (junction) in an electrical circuit, the sum of currents flowing into that node is equal to the sum of currents flowing out of that node, or:

The algebraic sum of currents in a network of conductors meeting at a point is zero.

Recalling that current is a signed (positive or negative) quantity reflecting direction towards or away from a node, this principle can be stated as:

[pic]

n is the total number of branches with currents flowing towards or away from the node.

This formula is valid for complex currents:

[pic]

The law is based on the conservation of charge whereby the charge (measured in coulombs) is the product of the current (in amperes) and the time (in seconds).

Kirchhoff’s Voltage Law

This law is also called Kirchhoff's second law, Kirchhoff's loop (or mesh) rule, and Kirchhoff's second rule.

The principle of conservation of energy implies that

The directed sum of the electrical potential differences (voltage) around any closed network is zero, or:

More simply, the sum of the emfs in any closed loop...

...Kirchhoff’sLaws
Gustav Kirchhoff, (1824-1887), was a German physicist who contributed greatly to the understanding of electrical circuits, spectroscopy, and the emission of black-body radiation. Kirchhoff formulated his famous circuit laws in 1845, while still a student at the University of Konigsberg, East Prussia. He completed this study as a seminar exercise, and it later became his doctoral dissertation.
Kirchhoff’sLaws include two basic principles. Kirchhoff’s First Law, also called Kirchhoff’s Current Law (KCL), states that at any node (junction) in an electrical circuit, the sum of all currents (Ik) flowing into that node is equal to the sum of currents flowing out of that node. In other words, the algebraic sum of all currents in a network of conductors meeting at a point is zero (Eq 1).
(Eq 1)
Kirchhoff’s Second Law, also called Kirchhoff’s Voltage Law (KVL), states that the sum of the voltage gains in any closed loop is equivalent to the sum of the voltage drops in that loop. In other words, the algebraic sum of the voltages (Vk) in a closed loop is equal to zero (Eq 2).
(Eq 2)
Equations (1) and (2) are interrelated, and this can be demonstrated through modeling a basic electrical circuit involving a second order, linear differential equation. For our basic...

...Cody Ross
8/8/14
Physics
Kirchhoff's Current Law is one of two fundamental laws in electrical engineering, the other being Kirchhoff's Voltage Law. Kirchhoff’s Current Law is a fundamental law, as fundamental as Conservation of Mass in mechanics, for example, because Kirchhoff’s Current Law is really conservation of charge.Kirchhoff's Voltage Law and Kirchhoff’s Current Law are the starting point for analysis of any circuit. Kirchhoff’s Current Law and Kirchhoff's Voltage Law always hold and are usually the most useful piece of information you will have about a circuit after the circuit itself. People and computer programs both use Kirchhoff's Voltage Law and Kirchhoff’s Current Law for circuit analysis. Kirchhoff's Current Law is not as complex as it might seem. All one really needs to know is that charge is conserved, so Kirchhoff's Current Law is really based on one simple fact: Charge can neither be created nor destroyed. From that basic fact we can get to Kirchhoff's Current Law. Despite that simplicity, it is a fundamental, widely used law that you need to...

...Ohm
Kirchoff's current and voltage laws
Ohm's law
Circuit analysis example
Bibliography
A little bit about the life and times of Gustav Robert Kirchoff:
Gustav Robert Kirchoff was a German physicist born on March 12, 1824, in Konigsber, Prussia. Gustav Kirchoff's first research topic was on the conduction of electricity. As a result of this research, Kirchoff wrote the Laws of Closed Electric Circuits in 1845. Theselaws were eventually named after their author, which are now known as Kirchoff's Current and Voltage Laws. Because Kirchoff's Voltage and Current laws apply to all electric circuits, a firm understanding of these fundamental laws is paramount in the understanding of how an electronic circuit functions. Although these laws have immortalized Kirchoff in the field of Electrical Engineering, Kirchoff also had additional discoveries. Gustav Kirchoff was the first person to verify that an electrical impulse traveled at the speed of light. Furthermore, Kirchoff made major contributions in the study of spectroscopy and he advanced the research into blackbody radiation. Gustav Robert Kirchoff died in Berlin in October 17, 1887.
Gustav Robert Kirchoff
(1824-1887)
http://www.ece.utexas.edu/~aduley/lab/
Home Page | A little history about...

...I. Title: Kirchhoff’sLaw
II. Objectives: To study the application of Kirchhoff’sLaw to a D.C. network by comparing the
observed and the computed values of the currents in the circuit.
III. Apparatus: Resistance Module, 1pc. Battery of two cells (3 volts), 1pc. Dry cell (1.5 volts),
Multitester, 4 pairs connectors
IV. Procedure with Experimental Setup:
Part A.
1.) The apparatus was arranged as in diagram 1. The switches were left open until it is checked.
2.) With the switches closed the voltages V1 and V2 across the batteries were measured with a voltmeter.
3.) Considering V1, V2, R1, R2 and R3 as known, the Kirchhoff’slaw was applied to the circuits and the correct number of independent current and voltage equations necessary to solve for the unknown current in each branch was written, that is one current equation and the fewest number of voltage equations that will include every emf and every resistance at least once in a set of equations. The equations for these currents were solved.
4.) Having calculated the current in each brach by an application of Kirchhoff’sLaws, the respective currents were measured experimentally. The circuit was break in turn in each branch and the ammeter was inserted in series to observe the values of the currents.
5.) The percentage error between the observed values of...

...Voltage: Ohm's Law and Kirchhoff's Rules
ABSTRACT
Ohm's Law and Kirchhoff's rules is fundamental for the understanding of
dc circuit. This experiment proves and show how these rules can be applied to
so simple dc circuits.
INTRODUCTION
In the theory of Ohm's Law, voltage is simply proportional to current as
illustrated in the proportionality, V=RI. As shown in this relation, V
represent voltage which is the potential difference across the two ends of a
electrical conductor and between which an electric current, I, will flow. The
constant, R, is called the conductor's resistance. Thus by the Ohm's Law, one
can determine the resistance R in a DC circuit without measuring it directly
provided that the remaining variable V and I is known.
A resistor is a piece of electric conductor which obeys Ohm's Law and
has been designed to have a specific value for its resistance. As an extension
of the Ohm's Law, two more relationship can be drawn for electric circuits
containing resistors connected in series or/and parallel. For resistors
connected in series, the sum of their resistance is, RTOTAL=R1+R2+ ..... +Rn .
And for resistors connected in parallel, 1/RTOTAL==1/R1+1/R2+ ..... +1/Rn .
Complex dc circuit involving a combination of parallel and series resistors can
be analyzed to find the current and voltage at each point of the circuit using 2
basic rules...

...as well as dissipating or converting it.
The electrical resistance per unit length, area, or volume of a substance is known as resistivity. Resistivity figures are often specified for copper and aluminum wire, in ohms per kilometer.
Opposition to AC, but not to DC, is a property known as reactance. In an AC circuit, the resistance and reactance combine vectorially to yield impedance.
Ohm's Law is the mathematical relationship among electric current, resistance, and voltage. The principle is named after the German scientist Georg Simon Ohm.
In direct-current (DC) circuits, Ohm's Law is simple and linear. Suppose a resistance having a value of R ohms carries a current of I amperes. Then the voltage across the resistor is equal to the product IR. There are two corollaries. If a DC power source providing E volts is placed across a resistance of R ohms, then the current through the resistance is equal toE/R amperes. Also, in a DC circuit, if E volts appear across a component that carries Iamperes, then the resistance of that component is equal to E/I ohms.
Mathematically, Ohm's Law for DC circuits can be stated as three equations:
E = IR
I = E/R
R = E/I
When making calculations, compatible units must be used. If the units are other than ohms (for resistance), amperes (for current), and volts for voltage), then unit conversions should be made before calculations are done. For example, kilohms should be converted to ohms, and...