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.
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.
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.
NO. of EQUATIONS No. of equations to be written are equal to the no. of loops or closed paths.
Example: We want to calculate the value of VR3 where values of VR1 and VR2 are known by using KVL.
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
+VR1 - 5 + VR2 – 15 +VR3 – 30 =0 which can be written as VR1+ VR2 +VR3 =5 +15 +30 = 50
Now suppose that VR1 and VR2 are known to be 18V and 12V respectively then VR3=20V
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.
Applying KVL to left loop VR1+ VR4 – 16 – 24 = 0 C + - Applying KVL to left loop VR1+ VR4 – 16 – 24 = 0
KVL equation for right loop starting at point B. C + - KVL equation for right loop starting at point B. VR2 + VR3 +8 +16 –VR4=0
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
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
we will use only linearly independent 8V C + - - - + + + - + - we will use only linearly independent equations to solve for all voltages.