Transcript Document
Physics 2112 Unit 9: Electric Current Today’s Concept: Electric Current Electricity & Magnetism Lecture 9, Slide 1 A Big Idea Review kq1q2 F1, 2 2 rˆ1, 2 r1, 2 Coulomb’s Law Force law between point charges Electric Field Force per unit charge Gauss’ Law Flux through closed surface is always proportional to charge enclosed Electric Potential Potential energy per unit charge Capacitance Relates charge and potential for two conductor system F E q 0 q2 Gauss’ Law Can be used to determine E field b U ab E dl q a Q C V r1,2 Electric Field Property of Space Created by Charges Superposition Qenc E dA Vab q1 F1,2 Spheres Cylinders Infinite Planes Electric Potential Scalar Function that can be used to determine E E V Electricity & Magnetism Lecture 9, Slide 2 Applications of Big Ideas Conductors Charges free to move Field Lines & Equipotentials What Determines How They Move? Spheres Cylinders Infinite Planes They move until E0! Gauss’ Law E 0 in conductor determines charge densities on surfaces Capacitor Networks Work Done By E Field b F dl qE dl b Wab a a Change in Potential Energy U a b Wa b qE dl b a Series: (1/C23) (1/C2) + (1/C3) Parallel C123 C1 + C23 Electricity & Magnetism Lecture 9, Slide 3 Key Concepts: 1) How resistance depends on A, L, s, r 2) How to combine resistors in series and parallel 3) Understanding resistors in circuits Today’s Plan: 1) Review of resistance & preflights 2) Work out a circuit problem in detail Electricity & Magnetism Lecture 9, Slide 4 I A s L Conductivity – high for good conductors. V Ohm’s Law: J s E Observables: V EL I JA I/A sV/L R Resistance R 1/s I V/R I V/(L/sA) R L sA Electricity & Magnetism Lecture 9, Slide 5 Civil Engineering Analogy I is like flow rate of water V is like pressure R is how hard it is for water to flow in a pipe L R sA To make R big, make L long or A small To make R small, make L short or A big Battery is like a pump Electricity & Magnetism Lecture 9, Slide 6 1 CheckPoint: Two Resistors 2 Same current through both resistors Compare voltages across resistors L R A L V IR A A2 4 A1 V2 14 V1 L2 2L1 V2 2V1 Electricity & Magnetism Lecture 9, Slide 7 CheckPoint: Current Density The SAME amount of current I passes through three different resistors. R2 has twice the cross-sectional area and the same length as R1, and R3 is three times as long as R1 but has the same cross-sectional area as R1. In which case is the CURRENT DENSITY through the resistor the smallest? Electricity & Magnetism Lecture 9, Slide 8 Circuit c b VB R1 E is conservative force go completely around circuit Vf = Vo R2 d a +VB V -IR1 -IR2 a b c d a Unit 9, Slide 9 Resistor Summary Series Parallel R1 R1 R2 R2 Wiring Each resistor on the same wire. Each resistor on a different wire. Voltage Different for each resistor. Vtotal V1 + V2 Same for each resistor. Vtotal V1 V2 Current Same for each resistor Itotal I1 I2 Different for each resistor Itotal I1 + I2 Increases Req R1 + R2 Decreases 1/Req 1/R1 + 1/R2 Resistance Electricity & Magnetism Lecture 9, Slide 10 CheckPoint: Resistor Network 1 Three resistors are connected to a battery with emf V as shown. The resistances of the resistors are all the same, i.e. R1= R2 = R3 = R. Compare the current through R2 with the current through R3: A. I2 > I3 B. I2 = I3 C. I2 < I3 Electricity & Magnetism Lecture 9, Slide 11 CheckPoint: Resistor Network 2 Three resistors are connected to a battery with emf V as shown. The resistances of the resistors are all the same, i.e. R1= R2 = R3 = R. Compare the current through R1 with the current through R2: A. I1/I2=1/2 B. I1/I2=1/3 C. I1 = I2 D. I1/I2=2 E. I1/I2=3 Electricity & Magnetism Lecture 9, Slide 12 CheckPoint: Resistor Network 3 Three resistors are connected to a battery with emf V as shown. The resistances of the resistors are all the same, i.e. R1= R2 = R3 = R. Compare the voltage across R2 with the voltage across R3: A. V2 > V3 B. V2 = V3 = V C. V2 = V3 < V D. V2 < V3 Electricity & Magnetism Lecture 9, Slide 13 R1 R2 R3 R CheckPoint 2 Compare the current through R1 with the current through R2 I1 I2 CheckPoint 3 CheckPoint 4 Compare the voltage across R2 with the voltage across R3 Compare the voltage across R1 with the voltage across R2 V2 V3 V1 V2 Electricity & Magnetism Lecture 9, Slide 14 CheckPoint: Resistor Network 4 Three resistors are connected to a battery with emf V as shown. The resistances of the resistors are all the same, i.e. R1= R2 = R3 = R. Compare the voltage across R1 with the voltage across R2. A. V1 = V2 = V B. V1 = 1/2 V2 = V C. V1 = 2V2 = V D. V1 =1/2 V2 =1/5 V E. V1 =1/2 V2 = 1/2 V Electricity & Magnetism Lecture 9, Slide 15 Example 9.1 R1 R2 In the circuit shown: V 18V, R1 1W, R2 2W, R3 3W, and R4 4W. R4 What is V2, the voltage across R2? V R3 Conceptual Analysis: Ohm’s Law: when current I flows through resistance R, the potential drop V is given by: V IR. Resistances are combined in series and parallel combinations Rseries Ra + Rb (1/Rparallel) (1/Ra) + (1/Rb) Strategic Analysis: Combine resistances to form equivalent resistances Evaluate voltages or currents from Ohm’s Law Expand circuit back using knowledge of voltages and currents Electricity & Magnetism Lecture 9, Slide 16 Example 9.1 R2 R1 V R2 R1 V R3 R24 R3 R4 R1 V V R234 R1234 Electricity & Magnetism Lecture 9, Slide 17 Quick Follow-Ups I1 R1 I2 R2 R1 I3 V R3 a V R234 R4 b What is I3 ? A) I3 2 A B) I3 3 A V3 = V234 = 12V C) I3 4 A I3 V3/R3 12V/3W 4A V 18V R1 1W R2 2W R3 3W R4 4W R24 6W R234 2W V234= 12V V2 = 4V I1234 = 6 Amps What is I1 ? We know I1 I1234 6 A I1 I2 + I3 Make Sense? Electricity & Magnetism Lecture 9, Slide 18 Power In Resistors Electro-Motive Force (EMF), Energy provided to make charges move, units of V dW dq dW dq Power dt dt =VI (for a battery) = I2R (for resistor) Unit 9, Slide 19 Example 9.2 R1 R2 In the circuit shown: V 18V, R1 1W, R2 2W, R3 3W, and R4 4W. R4 How much electrical energy does the battery put into the circuit every second in the previous problem? V R3 How much electrical energy does each resistor turn into thermal energy every second? 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 21