1. KIRCHHOFF’s VOLTAGE LAW
This law states that the algebraic sum of the voltages around any loop is zero. OR
Sum of voltages rises and voltage drops around any closed path or loop is equal to zero.

2. LOOP
It is the closed path for the flow of current in which no node is encountered more than one.
Loop can be considered as closed path in which work done in moving a unit charge is equal to zero.

3. ASSUMPTIONS
any increase in energy level is taken as positive and any decrease in energy level is taken as negative.
Current leaving the source is taken as positive and current entering the voltage source is taken as negative.

4. NO. of EQUATIONS
No. of equations to be written are equal to the no. of loops or closed paths.

5. Example:
We want to calculate the value of VR3
where values of VR1 and VR2 are known
by using KVL.

6. Now we will take increase in energy level
positive and decrease in energy level
negative. By using this assumption and
KVL the equation of this loop will be

7. +VR VR2 – 15 +VR3 – 30 =0
which can be written as
VR1+ VR2 +VR3 = = 50

8. Now suppose that VR1 and VR2 are
known to be 18V and 12V respectively
then VR3=20V

9. Note that this network has three closed paths
Example 8V C + -
Note that this network has three closed paths
the left loop, the right loop and outer loop.

10. Applying KVL to left loop VR1+ VR4 – 16 – 24 = 0C + -
Applying KVL to left loop
VR1+ VR4 – 16 – 24 = 0

11. KVL equation for right loop starting at point B. C + -
KVL equation for right loop starting at point B.
VR2 + VR –VR4=0

12. The equation for outer loop starting at point A 8V C + -
The equation for outer loop starting at
point A
VR1 +VR2 +VR3 + 8 – 24 =0

13. Note that if we add first two equations, we 8V C + - - - + + + - + -
Note that if we add first two equations, we
obtain the third equation. So these three
equations are not linearly independent. We
will discuss this issue in next lectures that

14. we will use only linearly independent 8V C + - - - + + + - + -
we will use only linearly independent
equations to solve for all voltages.