1. Circuit Principles Kirchhoff’s Current Law (KCL)
Conservation of charge
The algebraic sum of currents into a node is zero:
Sign convention:
+ current if into the node
- current if away from node.

2. 2. Kirchhoff’s Voltage Law (KVL)
Energy conservation around a closed loop
The algebraic sum of voltages around a loop is zero.
Sign Convention:
- sign of voltage is same as element’s polarity first encountered.

3. 4, 3, 1
Example 1. For the given circuit determine the current in all branches.

5. Connections Branch – represents a single element
Node – point of connection between two or more branches
Series connection – 2 elements exclusively share one node  same current
Parallel connection – connected to the same 2 nodes
Loop – a closed path formed by connecting branches.

6. Example: nodes, branches, loops
Original circuit
Equivalent circuit
How many branches, nodes and loops are there?

7. Example 2. Find vo and io.
Ans: 8V, 4A

8. 3. Network Reduction
A. n Resistors in Series:

9. Voltage-Divider Equation

10. B. n Resistors in parallel

11. Current-Divider Equation

12. Ex. 3. Find the equivalent resistance.
Ans: 14.4 

13. Example 4. Find: a) v1 and v2, b) power in the 3-k resistor, c) power supplied by the current source.

14. Ans: 15 V, 20 V, 75 mW, 200 mW

15. C. Wye-Delta Transformations

16. Example: Find the voltage V.

17. Derivations

18. Superimposed Y and Δ networks:
Each Y resistor is the product of the resistors in the two adjacent Δ branches, divided by the sum of the three Δ resistors.
Each Δ resistor is the sum of all possible products of Y resistors taken two at a time, divided by the opposite Y resistor.

19. Example: Find the voltage V.