Kirchoff’s Laws
Objective:
To determine the laws of Gustav Kirchoff.
How they are used to analyze an electronic circuit.
To illustrate how the laws work.
Introduction:
In 1845, German physicist Gustav Kirchhoff first described two laws that became central to electrical engineering. The laws were generalized from the work of Georg Ohm. The laws can also be derived from Maxwell’s equations, but were developed prior to Maxwell’s work.
The following descriptions of Kirchhoff's Laws assume a constant current. For timevarying current, or alternating current, the laws must be applied in a more precise method.
Body:
Kirchhoff's Current Law
Kirchhoff's Current Law, also known ...view middle of the document...
The voltage differences include those associated with electromagnetic fields (emfs) and resistive elements, such as resistors, power sources (i.e. batteries) or devices (i.e. lamps, televisions, blenders, etc.) plugged into the circuit.
Kirchhoff's Voltage Law comes about because the electrostatic field within an electric circuit is a conservative force field. As you go around a loop, when you arrive at the starting point has the same potential as it did when you began, so any increases and decreases along the loop have to cancel out for a total change of 0. If it didn't, then the potential at the start/end point would have two different values.
Positive and Negative Signs in Kirchhoff's Voltage Law
Using the Voltage Rule requires some sign conventions, which aren't necessarily as clear as those in the Current Rule. You choose a direction (clockwise or counterclockwise) to go along the loop.
When travelling from positive to negative (+ to ) in an emf (power source) the voltage drops, so the value is negative. When going from negative to positive ( to +) the voltage goes up, so the value is positive.
When crossing a resistor, the voltage change is determined by the formula I*R, where I is the value of the current and R is the resistance of the resistor. Crossing in the same direction as the current means the voltage goes down, so its value is negative. When crossing a resistor in the direction opposite the current, the voltage value is positive (the voltage is increasing).
Sign conventions for Kirchhoff's loop rule 

Kirchhoff's Voltage Law in action
If you click on the picture to the right, you can advance to a second picture that depicts a loopabcd. If you begin at a and advance clockwise along the interior loop, the Voltage Law yields the equation:
v1 + v2 + v3 + v4 = 0
In this case, the current will also be clockwise. Crossing the resistors will result in v1, v2, andv3 all being negative. Since you're crossing from negative to...