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Physics 2112 Unit 10: Kirchhoff’s Rules Today’s Concept: Kirchhoff’s Rules Electricity & Magnetism Lecture 10, Slide 1 Kirchhoff’s Laws: Why use them? R1 R3 V1 V2 R2 How Can We Solve This One? R1 R3 V1 V2 R2 = V I1234 R12 THE ANSWER: Kirchhoff’s Rules Electricity & Magnetism Lecture 10, Slide 2 Based on two concepts V = 0 i Kirchhoff'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. I in = I out Kirchhoff'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. Electricity & Magnetism Lecture 10, Slide 3 Two Ways to do the algebra R1 V1 I1 R1 R3 V2 R3 I3 V 1 I2 R2 Method #1 current in every leg 3 equations, 3 unknowns I1 I2 R2 V2 Method #2 “current” in every loop 2 equations, 2 unknowns Electricity & Magnetism Lecture 10, Slide 4 We will use second method 1) Choose loops and direction Place “current” in each one 2) Write down voltage drops and gains 3) Across a battery: – to + is a voltage gain, + to – is a drop 4) Across a resistor: with the current is a voltage drop, against the current voltage gain A - + + + R2 + E1 - B I1 E3 I2 - + E2 - R3 R5 - I3 + + R4 + I5 Electricity & Magnetism Lecture 10, Slide 5 Choosing Loops Doesn’t as long as every element is in at least one loop A - + + + R2 + E1 - B I1 E3 - - I2 - + E2 A R3 R5 - I3 + + - + - + + + R2 + E1 - B I1 E3 - - R4 R3 R5 I5 - I2 + E2 I3 - + + + I5 Electricity & Magnetism Lecture 10, Slide 6 CheckPoint: Gains and Drops In the following circuit, consider the loop abc. The direction of the current through each resistor is indicated by black arrows. If we are to write Kirchhoff'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) b) c) d) e) drop, drop, drop gain, gain, gain drop, gain, gain gain, drop, drop drop, drop, gain Electricity & Magnetism Lecture 10, Slide 7 Example 10.1 1 2 2V 1V 1 In this circuit, assume Vi and Ri are known. IM What is IM ? 1V Conceptual Analysis: – Circuit behavior described by Kirchhoff’s Rules: • KVR: S Vdrops = 0 Strategic Analysis – – Write down Loop Equations (KVR) Solve Electricity & Magnetism Lecture 10, Slide 8 Calculation 1 2 1 2V Choose Loops and put currents in them. 1V I2 1V Electricity & Magnetism Lecture 10, Slide 9 Example 10.2 I2 4=R1 6=R3 12V In this circuit, what is the current o battery ? I1 3=R2 Conceptual Analysis: – Circuit behavior described by Kirchhoff’s Rules: • KVR: S Vdrops = 0 Strategic Analysis – – Write down Loop Equations (KVR) Solve Electricity & Magnetism Lecture 10, Slide 10 Redraw circuit 4=R1 6=R3 12V 3=R2 3=R2 6=R3 12V 4=R1 Electricity & Magnetism Lecture 10, Slide 11 CheckPoint: Circuits w/ Resistors and a Battery 1 Consider the circuit shown below. Which of the following statements best describes the current flowing in the blue wire connecting points a and b? A. Positive current flows from a to b B. Positive current flows from b to a C. No current flows between a and b Electricity & Magnetism Lecture 10, Slide 12 Prelecture What is the same? CheckPoint Current flowing in and out of the battery. 2R 3 2R 3 What is different? Current flowing from a to b. Electricity & Magnetism Lecture 10, Slide 13 I 2/ 3I R 1/ 3I a V 2/ 2/ I 3 3I b R 1/ 3I V/2 2R 1/ 1/ 03I 12/ I 3 2R 1/ 3I 2/ 3I 3I Electricity & Magnetism Lecture 10, Slide 14 CheckPoint: Circuits w/ Resistors and a Battery 2 Consider the circuit shown below. In which case is the current flowing in the blue wire connecting points a and b bigger? (A) Case A (B) Case B (C)They are the same Electricity & Magnetism Lecture 10, Slide 15 Parallel and Series (with color) R1 R2 V R3 R4 If every electron that goes through one element must go through another, those two are in series. If two sides of two elements can be connected by different colored lines, those two are in parallel. . If two points are connected by a line not containing any circuit elements those point are at the same potential. Unit 9, Slide 16 Example 10.3 0.1 3V 2 2 A battery has an EMF of 3V and an internal resistance of 0.1. It is hooked in parallel to two light bulbs which both that a resistance of 2 when hot. What would a voltmeter read if it was connected to across the terminals of the battery when a) Both switches were open? b) When one switch is closed? c) When both switches are closed? Unit 10, Slide 17