Transcript Document
Physics 212 Lecture 10 Today's Concept: Kirchhoff’s Rules Circuits with resistors & batteries Physics 212 Lecture 10, Slide 1 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 Physics 212 Lecture 10, Slide out of the node. 2 Physics 212 Lecture 10, Slide 3 Kirchoff’s Voltage Rule V i 0 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. WHY? The potential difference between a point and itself is zero ! Physics 212 Lecture 10, Slide 4 Kirchoff’s Current Rule I in I out 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. WHY? Electric Charge is Conserved Physics 212 Lecture 10, Slide 5 Kirchhoff’s Rules (1) Label all currents R1 (2) Label +/- for all elements A R2 (3) Choose loop and direction (4) Write down voltage drops E3 B E1 E2 R3 R4 R5 (5) Write down node equation Physics 212 Lecture 10, Slide 17 6 Checkpoint 2 GAIN In the following circuit, consider the loop abc. The direction of the current through each resistor is indicated by black arrows. DROP 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 A. B. gain, gain, gain C. drop, gain, gain B D. E. gain, gain, drop C gain, drop, drop D E With the current VOLTAGE DROP Against the current VOLTAGE GAIN Physics 212 Lecture 10, Slide 7 Physics 212 Lecture 10, Slide 8 R1 R2 V1 V2 I1 I2 Calculation In this circuit, assume Vi and Ri are known. What is I2 ?? R3 V3 I3 • Conceptual Analysis: •Strategic Analysis Physics 212 Lecture 10, Slide 9 Physics 212 Lecture 10, Slide 10 Follow-Up 2V R V 2R a I1 I2 b R V I3 • Suppose we short R3: (A) (B) (C) (D) Vab remains the same Vab changes sign Vab increases Vab goes to zero • We know: – – – I2 = I1 = I3 = What happens to Vab (voltage across R2?) Physics 212 Lecture 10, Slide 11 Checkpoint 3a Consider the circuit shown below. Note that this question is not identical to the similar looking one I1 I2 you answered in the prelecture. Which of the following best describes the current flowing in the blue wire connecting points a and b? Physics 212 Lecture 10, Slide 12 Consider the circuit shown below. Checkpoint 3b In which case is the current flowing in the blue wire connecting points a and b the largest? A. Case A B. Case B C. They are both the same Physics 212 Lecture 10, Slide 13 Physics 212 Lecture 10, Slide 14 Prelecture Checkpoint Things that are the same: Things that are different: Physics 212 Lecture 10, Slide 15 Batteries Ideal Battery: Voltage always V0 independent of R Real Battery: + r R VL V0 Physics 212 Lecture 10, Slide 16