# Kirchhoff’s voltage law

Kirchhoff’s Voltage Law (KVL) is very fundamental law in basic electrical engineering. Electrical Circuits are basically of two types- series and parallel. Generally, KVL is used in series circuits whereas Kirchhoff’s Current Law (KCL) is used in parallel circuits. By applying KVL, we can easily solve the unknown voltages without knowing the value of resistance and circuit current.

*KVL states that the algebraic sum of the voltage rises and drops around a closed loop (or path) is zero.*

Here, *abcda *is a closed loop. A plus sign is assigned to a potential rise (− to +), and a minus sign to a potential drop (+ to −). According to above figure, from point *a, *we first encounter a potential drop *V*_{1} (+ to −) across *R*_{1} and then another potential drop *V*_{2} across *R*_{2}. Continuing through the voltage source, we have a potential rise *E *(− to +) before returning to point *a. *In symbolic form, where Σ represents summation, the closed loop, and *V *the potential drops and rises, we have according to KVL:

From the figure, KVL produces the following equation according to clockwise direction:

+E−V_{1}−V_{2}=0

or , E= V_{1}+V_{2}

which means that the applied voltage of a series circuit equals the sum of the voltage drops across the series elements.

Kirchhoff’s voltage law can also be stated in the following form:

which in words states that the sum of the rises around a closed loop must equal the sum of the drops in potential.

We get the similar results, if we apply the KVL to anti-clockwise direction in above figure.

**Example:**

Applying KVL, we get the result of unknown voltage V_{1} from the above circuit. First of all, taking the KVL equation according to clockwise direction:

+E_{1}−V_{1}−4.2V−E_{2}=0

or, +16V−4.2V−9V= V_{1}

or, **V _{1} = 2.8V**