1. 1 Kirchhoff’s Law

2. KIRCHHOFF’S LAWS Ohm’s law by itself is insufficient to analyze circuits. However, when combined with Kirchhoff’s two laws, we have a powerful set of tools to analyze a large variety of circuits. Kirchhoff Current Law (KCL) Kirchhoff Voltage Law (KVL) 2

3. Kirchhoff’s Law Network topology A branch represents a single element such as a voltage source or a resistor. 3

4. Network topology A node is the point of connection between two or more branches. Kirchhoff’s Law 4

5. Network topology A loop is any closed path in a circuit. Kirchhoff’s Law 5

6. Network topology Two or more elements are in series if they exclusively share a single node and consequently share the same current Two or more elements are in parallel if they are connected to the same two nodes and consequently have the same voltage across them 1  & 2  - parallel 10V & 4  - parallel 5  in series with (1  and 2  in parallel) Kirchhoff’s Law 6

7. 7 Two or more nodes connected just by wires can be considered as one single node. Nodes Connected by Wires Only Group of nodes connected only by wires One big node A single node This network has three nodes

8. i1i1 i2i2i2i2 i3i3i3i3 node i 1 i 1 flows into the node i 2 i 2 flows out of the node i 3 i 3 flows out of the node i 1 = i 2 + i 3 KIRCHHOFF’S CURRENT LAW Sometimes Kirchhoff’s Current Law is abbreviated just by KCL The sum of currents flowing into a node must be balanced by the sum of currents flowing out of the node. 8

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10. 10 Node a Node b

11. EXAMPLE Voltage source supplies a current of 3 A, and current passing thru R2 is 2A, compute the current thru R3 11 Answer: 6A

12. 12 Example How much are the currents i 1 and i 2 ? + _ i1i1 4 mA i2i2 10 mA 3 mA 4 mA + 3 mA + 7 mA = 14 mA node i 2 = 10 mA – 3 mA = 7 mA i 1 = 10 mA + 4 mA = 14 mA

13. KIRCHHOFF'S VOLTAGE LAW (KVL) Loop: A loop is a set of branches forming a closed path. 13 The algebraic sum of the voltages around any loop or closed path in an electric circuit is zero.

14. 14 6V but opposite reference polarity!

15. 15 The voltage measured between any two nodes does not depend of the path taken. Example of KVL: v1= v1= v1= v1= v 2 v 2 + v3v3v3v3 Similarly: v1= v2 + v4 and: v3= v3= v3= v3= v4v4v4v4 + _ v 2 + v 2 – +v3v3 –+v3v3 – +v4v4 –+v4v4 – + ++v1v1 – –++v1v1 – – – voltage KIRCHHOFF'S VOLTAGE LAW (KVL)

16. 16 How much is the voltage V o ? V o = 3.1 V + 6.8 V VoVoVoVo _ + + 3.1V – + 6.8 V 6.8 V– Example v 4 = 6.8 V v 4 = 6.8 V How much is the voltage v 4 ?+ ++v4v4__++v4v4___

17. 17 Example v 1 v 5 v 2, v 3,v 4 If v 1 = 10 V and v 5 = 2 V, what are v 2, v 3, and v 4 ? v 2 = 10 V v 3 = 10 V – 2 V = 8 V v 4 = 2 V v 4 = 2 V + _ + v 1 = 10 V – + ++v2v2––++v2v2–––+ ++v4v4––++v4v4––– + v 5 = 2 V – + v 3 –

18. 18 Find I R1, V R2, R 4 Example

19. Use Ohm’s law, KVL and KCL to find V x EXAMPLE 19 Ohm’s Law: V R4 = (1A)(5  ) = 5V = V R2 = V R3 I R2 = 5V/10  = 0.5A I R3 = 5V/5  = 1A KCL:I T = I R2 + I R3 + I R4 = 0.5A + 1A + 1A = 2.5A Ohm’s Law: V R1 = I T R 1 = (2.5A)(5  ) = 12.5V KVL: V x = V R1 + V R4 = 12.5V+5V = 17.5V

20. EXAMPLE Find i x and i y 20

21. EXAMPLE Find V s and V x 21