Kirchoff's Voltage Law (KVL)

"The sum of all the voltages around a closed loop is equal to zero."

Or we can say that the algebraic sum of all voltage rises is equal to algebraic sum of all the voltage drops around the closed loop. In Figure, consider mesh BEDB, according to KVL
 
Example

In each circuit diagrams in Figure drawn below, write the mesh equations by using KVL
 
Circuit diagrams to demonstrate application of KVL in above example.

Figure (a) contains a single loop thus a single current, I is flowing around it. Hence a single equation will result as stated below
    
If V_s, R₁ and R₂ are known to us, then I can be found.

Figure (b) contains 2 meshes with currents I₁ and I₂ hence there will be 2 equations as shown below. Note that the branch containing R₂ is common to both meshes with the currents I₁ and I₂ ?owing in the opposite directions.
 

Given V_s, R₁, R₂ , R₃, Equations stated above can be solved simultaneously to evaluate I₁ and I₂.

For the circuit diagram of Figure (c), 3 equations are required to be written as follows. Also note that there is no circuit element shared among loops 2 and 3 thus I₂ and I₃ are independent of each other.
 

If V_s and resistors' values are known, the mesh currents can be evaluated by solving Equations obtained above at the same time.

Resistors in Series

Consider Figure  given below with one voltage source and 2 resistors connected in series to form the single mesh with current I.

Figure--Series combination of 2 resistors.

According to KVL

Vs= V1+V2

By using Ohm's law V= IR from,

IR_eq =IR₁+ IR₂

R_eq= R₁+ R₂

here R_eq is the combined or equivalent resistance of series network. Thus the equivalent resistance of 2 or more resistors connected in series can be given by the algebraic sum of all resistances.

Generally, for n number of serial resistors, R can be given by

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