1. Physics 212 Lecture 10, Slide 1 Physics 212 Lecture 10 Today's Concept: Kirchhoff’s Rules Circuits with resistors & batteries

2. Main Point There really is only one main point in this lecture: namely that to analyze any circuit, we only need apply two rules: Kirchhoff’s Voltage and Current Rules. Kirchhoff’s Voltage Rule is essentially a statement of the conservation of energy: namely, if you start at any point on a circuit, and follow that circuit around a complete loop, returning to where you started, the net change in the electric potential is zero. Kirchhoff’s Current Rule is essentially a statement of charge conservation: namely, the sum of the currents flowing into the node of the circuit is equal to the sum of the currents flowing out of the node. Physics 212 Lecture 10, Slide 2

3. Physics 212 Lecture 10, Slide 3

4. Physics 212 Lecture 10, Slide 4 Kirchoff's Voltage Rule states that the sum of the voltage changes caused by any elements (like wires, batteries, and resistors) around a circuit must be zero. Kirchoff’s Voltage RuleWHY? The potential difference between a point and itself is zero !

5. Physics 212 Lecture 10, Slide 5 Kirchoff's Current Rule states that the sum of all currents entering any given point in a circuit must equal the sum of all currents leaving the same point. Kirchoff’s Current RuleWHY? Electric Charge is Conserved

6. Physics 212 Lecture 10, Slide 6 Kirchhoff’s Rules (1)Label all currents (2)Label +/- for all elements (3) (3)Choose loop and direction (4) (4)Write down voltage drops R4R4 R1R1 E1E1 R2R2 R3R3 E2E2 E3E3 R5R5 A B 17 (5) (5)Write down node equation

7. Physics 212 Lecture 10, Slide 7 Checkpoint 2 A B C D E With the current VOLTAGE DROP Against the current VOLTAGE GAIN If we are to write Kirchoff's voltage equation for this loop in the clockwise direction starting from point a, what is the correct order of voltage gains/drops that we will encounter for resistors R1, R2 and R3? A. drop, drop, drop B. gain, gain, gain C. drop, gain, gain D. gain, drop, dropE. gain, gain, drop GAIN In the following circuit, consider the loop abc. The direction of the current through each resistor is indicated by black arrows. DROP

8. Physics 212 Lecture 10, Slide 8

9. Physics 212 Lecture 10, Slide 9Calculation V1V1 R1R1 R2R2 In this circuit, assume V i and R i are known. What is I 2 ?? R3R3 V2V2 V3V3 I1I1I1I1 I3I3I3I3 I2I2I2I2 Conceptual Analysis: Strategic Analysis

10. Physics 212 Lecture 10, Slide 10

11. Physics 212 Lecture 10, Slide 11Follow-Up We know: – –I 2 = – –I 1 = – –I 3 = 2V R 2R R V V I1I1I1I1 I3I3I3I3 I2I2I2I2 a b Suppose we short R 3 : What happens to V ab (voltage across R 2 ?) (A)V ab remains the same (B)V ab changes sign (C)V ab increases (D)V ab goes to zero R

12. Physics 212 Lecture 10, Slide 12 I1I1 I2I2 Checkpoint 3a Consider the circuit shown below. Note that this question is not identical to the similar looking one you answered in the prelecture. Which of the following best describes the current flowing in the blue wire connecting points a and b?

13. Physics 212 Lecture 10, Slide 13 Checkpoint 3b Consider the circuit shown below. In which case is the current flowing in the blue wire connecting points a and b the largest? A. Case AB. Case BC. They are both the same

14. Physics 212 Lecture 10, Slide 14

15. Physics 212 Lecture 10, Slide 15 Prelecture Checkpoint Things that are the same: Things that are different:

16. Physics 212 Lecture 10, Slide 16 r V0V0 + VLVL R Batteries Ideal Battery: Voltage always V 0 independent of R Real Battery: