Example: Node, Paths, Loops and Branches Kirchhoff’s Current Law (KCL) KCL Problems Home Work Problems

1. Basic Electric Circuits – © 2020 Mouli Sankaran Email: mouli.sankaran@yahoo.com

2. Basic Electric Circuits – © 2020 Mouli Sankaran Email: mouli.sankaran@yahoo.com 2
Session 4B: Focus
 Example: Node, Paths, Loops and Branches
 Kirchhoff’s Current Law (KCL)
 KCL Problems
 Home Work Problems

3. Basic Electric Circuits – © 2020 Mouli Sankaran Email: mouli.sankaran@yahoo.com
Nodes, Paths, Loops and Branches

4. Basic Electric Circuits – © 2020 Mouli Sankaran Email: mouli.sankaran@yahoo.com 4
Definitions: Branch and Mesh
 Branch: A single path, containing one simple
element, which connects one node to any other node
 Mesh: A loop which does not contain any other loops
within it
H G
F
E
D
C
B
A
Node or Path or Loop or Mesh or Branch?
A : Node
A > B : Branch
A > B>F>G>C>D>A : Loop, not a
Mesh
B>F>G>C>B : Mesh
A>B>C>E>A : Mesh

5. Basic Electric Circuits – © 2020 Mouli Sankaran Email: mouli.sankaran@yahoo.com
Kirchhoff’s Current Law (KCL)

6. Basic Electric Circuits – © 2020 Mouli Sankaran Email: mouli.sankaran@yahoo.com 6
Kirchhoff’s Current Law (KCL)
 Let us study two laws named after Gustav Robert
Kirchhoff (two h’s and two f ’s)
◦ A German university professor who was born about the time
Ohm was doing his experimental work
 KCL states that the algebraic sum of the currents
entering any node is zero
 This law represents a mathematical statement of the
fact that charge cannot accumulate at a node.
 A node is not a circuit element, and it certainly
cannot store, destroy, or generate charge.
 Hence, the currents must sum to zero at any node in the
circuit

7. Basic Electric Circuits – © 2020 Mouli Sankaran Email: mouli.sankaran@yahoo.com 7
KCL
 Similarly, this law could equally be well applied to the
algebraic sum of the currents leaving the node
iA + iB + (- iC ) + (- iD ) = 0
 The algebraic sum of the four currents entering the
node must be zero:
(-iA ) + (-iB) + iC + iD = 0

8. Basic Electric Circuits – © 2020 Mouli Sankaran Email: mouli.sankaran@yahoo.com 8
KCL
iA + iB = iC + iD
• We might also wish to equate the sum of the currents
having reference arrows directed into the node to the
sum of those directed out of the node:

9. Basic Electric Circuits – © 2020 Mouli Sankaran Email: mouli.sankaran@yahoo.com 9
Problem 1: KCL
 Compute the current through resistor R3
◦ If the voltage source supplies a current of 3 A
 Current i =
Note: This is Example problem 3.1 on page 41, Figure 3.3 in the Ref 1 book (by Hayt)
6 A
3 A
iR1 + 5 = 2 + i
3 + 5 = 2 + i
3 + 5 - 2= i
i = 6 A
Total current entering the node A = Total current leaving the node A
Node A
Reference node

10. Basic Electric Circuits – © 2020 Mouli Sankaran Email: mouli.sankaran@yahoo.com 10
Problem 2: KCL
 (a) Find I1 :
 (b) Find I1 : I2 :
6 mA
Note: This problem is E 2.5 on
page 35, Figure E 2.5 in the Ref 2
book (by Irwin)
8 mA 5 mA

11. Basic Electric Circuits – © 2020 Mouli Sankaran Email: mouli.sankaran@yahoo.com 11
Problem 3: KCL
 Write the KCL equations for the circuit below.
Note: This is Example 2.7 on page 33, Figure 2.7 in the Ref 2 book (by Irwin)
i5 = i2 + i1
At Node 1:
i2 + 50i2 = i3
At Node 2:
i1 = 50i2 + i4At Node 3:
How many nodes are there?
How many KCL equations to be
written?
No KCL equation for the reference node (4)
4
3
Which is the reference node? 4

12. Basic Electric Circuits – © 2020 Mouli Sankaran Email: mouli.sankaran@yahoo.com
Home Work Problems

13. Basic Electric Circuits – © 2020 Mouli Sankaran Email: mouli.sankaran@yahoo.com 13
S4.2_HW_Problem_1
 (a) Find I1 :
 (b) Find IT:
-50 mA
Note: This problem is E 2.4 on
page 35, Figure E 2.4 in the Ref 2
book (by Irwin)
70 mA

14. Basic Electric Circuits – © 2020 Mouli Sankaran Email: mouli.sankaran@yahoo.com 14
S4.2_HW_Problem_2
 (a) Find Ix :
 (b) Find Ix :
4 mA
Note: This problem is E 2.6 on
page 35, Figure E 2.6 in the Ref 2
book (by Irwin)
12 mA

15. Basic Electric Circuits – © 2020 Mouli Sankaran Email: mouli.sankaran@yahoo.com 15
S4.2_HW_Problem_4
 How many nodes and braches are there?
 Find RA =
Note: This is Practice 3.1 on page 42, Figure 3.4 in the Ref 1 book (by Hayt)
1 Ω
8 + 13 = iRA + ix
Total current entering the node A = Total current leaving the node A
= 3A
8 A
Nodes = 3
Branches = 5
18 V
Node A
At Node A:
iRA
21 = iRA + 3
iRA = 18
RA = VRA / iRA = 18/18
RA = 1 ΩGND or Reference Node

16. Basic Electric Circuits – © 2020 Mouli Sankaran Email: mouli.sankaran@yahoo.com 16
Session 4B: Summary
 Example: Node, Paths, Loops and Branches
 Kirchhoff’s Current Law (KCL)
 KCL Problems
 Home Work Problems

17. Basic Electric Circuits – © 2020 Mouli Sankaran Email: mouli.sankaran@yahoo.com 17
References
Ref 1 Ref 2