Kirchhoff's Voltage Law describes the distribution of voltage within a loop, or closed conducting path, of an electrical circuit. Specifically, Kirchhoff's Voltage Law states that:
The algebraic sum of the voltage (potential) differences in any loop must equal zero.
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 counter-clockwise) 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).
Kirchhoff's Voltage Law in action:
depicts a loop abcd. 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, and v3 all being negative. Since you're crossing from negative to positive, v4 will be positive. If you consider the dotted line that has the R5 resistor, you get a total of three loops in the circuit. The first one has already been described. One loop is the largest loop and another is the smallest loop at the bottom, to yield the equations:
v1 + v2 + v5 + v4 = 0 (abcd taking the new path instead of R5)
v3 + v5 = 0 (the small loop cd)
The second equation indicates that v3 = -v5. This makes sense, because both currents will be travelling from c to d, so on the small loop you'll cross one resistor with the current and the other resistor against the current. If the resistors are of equal value, then the current in both paths will be equal.
