1. Lecture 2 2.1 Sources 2.2 Ohm’s Law 2.4 Kirchhoff’s Laws

2. Voltage and Current Sources

3. Independent Sources

4. Characteristics An independent source establishes a voltage or current in a circuit without relying on voltages and currents elsewhere in the circuit. The value of the voltage or current supplied is specified by the value of the independent source alone.

5. Exercise

6. Electrochemistry of a Lemon Battery Zn→Zn 2+ +2e - Cu 2+ +2e - →Cu Add standard reduction potential to obtain the voltage across the terminals. +0.76 V +0.34 V Net: 1.10 V - + e-e-

7. Typical Values 1 Lemon – 0.9 Volts – 300 uA – 270 uW Red LED: – 1.7 V – 500 uA – 850 uW, i.e. 3 lemons in series

8. Ohm’s Law

9. Analogy The height of the water=voltage The volume of flow through the hole per second=current The smallness of the hole = resistance Water wheel hit by the flow from the hole = power

10. Thought Experiment #1 Fixed hole dimension↔ Fixed R Height of water↑ → flow rate↑. V↑ → I↑

11. Thought Experiment #2 Fixed height of water↔ Fixed V Hole dimension↑ → flow rate↑ R↓ → I↑

12. Derivation of Ohm’s Law Three variables: V,I and R. Different Possibilities: – V=IR (1) – I=VR (2) – R=VI (3) Intuition – If R is constant, V↑ → I↑. (3) is not possible. (1) and (2) are possible. – If V is constant, R↓ → I↑. (2) and (3) are not possible

13. Ohm’s Law V=IR Mnemonic: Victory Is Rare V represents the voltage difference between the two terminals of a resistor!

14. Exercise Calculate the value v a Determine the power dissipated in the resistor

15. Exercise ` Current is equal to 50V/25 Ohms=2A The battery provides -100W of power. The resistor uses +100 W of power.

16. My Favorite Quiz Question What is the current through the 25 Ohm resistor? Current =(50V-25V)/25 Ohms=1A

17. Current Flows from a point of High potential to a point of Low potential

18. Problem 2.21 Label the (+) and (-) terminal of the 65 Ω s and 50 Ω given the assumed direction of i 0 and i 1.

19. Kirchhoff’s Laws

21. KCL Kirchhoff’s Current law (KCL) – The algebraic sum of all the currents at any node in a circuit equals zero

22. Bipolar Junction Transistor Example I E =I B +I C Bipolar Junction Transistor Electronics I (ES230)

23. A Voltage Adder Using an Operational Amplifier (Application: Noise Cancellation) I R1 I R2 IRFIRF KCL: I R1 +I R2 =I RF Class: ES220

24. KVL Kirchhoff’s Voltage Law – The algebraic sum of all the voltage around any closed path in a circuit equals zero

25. Exercise Sum the voltages around each designated path in the circuit

26. Example 2.8 1.KCL at b 2.KVL around cabc loop 3.Solve for i o and i 1

27. Problem 2.18 1.KCL at the top node 2.KVL around the right loop 3.Find i 1, i 2, v o