Wednesday, August 17, 2011

## Kirchhoff Laws

Gustav Robert Kirchhoff

Kirchhoff was a German physicist born on March 12, 1824, in Königsberg, Prussia. His first research was on the conduction of electricity, which led to his presentation of the laws of closed electric circuits in 1845. Kirchhoff’s current law and Kirchhoff’s voltage law apply to all electrical circuits and therefore are fundamentally important in understanding circuit operation. Kirchhoff was the first to verify that an electrical impulse travelled at the speed of light. Although these discoveries have immortalized Kirchhoff’s name in electrical science, he is better known for his work with R. W. Bunsen in which he made major contributions in the study of spectroscopy and advanced the research into black body radiation. Kirchhoff died in Berlin on October 17, 1887.

Kirchhoff’s Voltage Law

Next to Ohm’s law, one of the most important laws of electricity is Kirchhoff’s voltage law (KVL) which states the following:

The summation of voltage rises and voltage drops around a closed loop is equal to zero.

Symbolically, this may be stated as follows:

In the above symbolic representation, the uppercase Greek letter sigma stands for summation and V stands for voltage rises and drops. A closed loop is defined as any path which originates at a point, travels around a circuit, and returns to the original point without retracing any segments.

An alternate way of stating Kirchhoff’s voltage law is as follows:

The summation of voltage rises is equal to the summation of voltage drops around a closed loop.

If we consider the above circuit, we may begin at point a in the lower left-hand corner. By arbitrarily following the direction of the current, I, we move through the voltage source, which represents a rise in potential from point a to point b. Next, in moving from point b to point c, we pass through resistor R1, which presents a potential drop of V1. Continuing through resistors R2 and R3, we have additional drops of V2 and V3 respectively. By applying Kirchhoff’s voltage law around the closed loop, we arrive at the following mathematical statement for the given circuit:

E- V1  - V2 - V3 =0

Although we chose to follow the direction of current in writing Kirchhoff’s voltage law equation, it would be just as correct to move around the circuit in the opposite direction. In this case the equation would appear as follows:

V3  + V2 + V1 - E =0

Example:

E1 - V1 + E2- V2 - V3 +E3 = 0

Kirchhoff’s Current Law

Recall that Kirchhoff’s voltage law was extremely useful in understanding the operation of the series circuit. In a similar manner, Kirchhoff’s current law is the underlying principle which is used to explain the operation of a parallel circuit. Kirchhoff’s current law states the following:

The summation of currents entering a node is equal to the summation of currents leaving the node.

An analogy which helps us understand the principle of Kirchhoff’s current law is the flow of water. When water flows in a closed pipe, the amount of water entering a particular point in the pipe is exactly equal to the amount of water leaving, since there is no loss. In mathematical form, Kirchhoff’s current law is stated as follows:

Above figure is an illustration of Kirchhoff’s current law. Here we see that the node has two currents entering, I1 =5 A and I5 =3 A, and three currents leaving, I2 =2 A, I3 =4 A, and I4 =2 A.

5 A  + 3 A = 2 A  + 4 A + 8 A
8 A  = 8 A

## The Beauty of the World

The Beauty of the World