2. Example 1

3. Example 2 Allowed Not Allowed

4. Example 3

5. Example 4

6. Example 5 Allowed Not Allowed

7. Current Sources in Series

8. Series and Parallel Sources Voltage sources in series can be combined into a single voltage source:  Current sources in parallel can be combined into a single current source: Ia + Ib + Ic Va+Vb+Vc Va Vb Vc IaIbIc

9. Independent Sources Independent voltage source maintains the prescribed voltage across its terminals regardless of the current drawn from it Independent current source maintains the prescribed current through its terminals regardless of the voltage across those terminals

10. “Controlled” or “Dependent” Sources A voltage or current source whose value “depends” on the value of voltage or current elsewhere in the circuit Use a diamond-shaped symbol

11. Dependent Voltage Sources +–+– 6Vx6Vx Voltage-Controlled Voltage Source (VCVS) 6000I x Current-Controlled Voltage Source (CCVS) +–+–

12. Dependent Current Sources 0.006V x Voltage-Controlled Current Source (VCCS) 6Ix6Ix Current-Controlled Current Source (CCCS)

13. Practical Dependent Sources Operational amplifiers Transistors Bipolar Junction Transistors (BJTs) Metal-Oxide-Semiconductor Field Effect Transistors (MOSFETs) Voltage and current regulators Other devices include: Photodetectors, LEDs, and lasers Piezoelectric devices Thermocouples, thermovoltaic sources

15. Star - Delta Transformation:

16. Q: Q: Find the resistance between the points E and F ?

17. Solution

18. Ans. : 5.6 Ω

19. Home Work Q 1 : Find R ab and I ?

20. Q2 : Use  -to-Y transformation to find the voltages v 1 and v 2 ?

21. Q 3 :Find the total resistance in the circuit below?