Physics 2112 Unit 9: Electric Current Today’s Concept: Electric Current

A Big Idea Review Coulomb’s Law Force law between point charges q1 q2 Electric Field Force per unit charge Property of Space Created by Charges Superposition Gauss’ Law Flux through closed surface is always proportional to charge enclosed Gauss’ Law Can be used to determine E field Spheres Cylinders Infinite Planes Electric Potential Potential energy per unit charge Electric Potential Scalar Function that can be used to determine E Capacitance Relates charge and potential for two conductor system 2

Applications of Big Ideas Conductors Charges free to move What Determines How They Move? They move until E = 0 ! E = 0 in conductor determines charge densities on surfaces Spheres Cylinders Infinite Planes Gauss’ Law Field Lines & Equipotentials Field Lines Equipotentials Capacitor Networks Series: (1/C23) = (1/C2) + (1/C3) Parallel C123 = C1 + C23 Work Done By E Field Change in Potential Energy 3

Key Concepts: Today’s Plan: How resistance depends on A, L, s, r How to combine resistors in series and parallel Understanding resistors in circuits Today’s Plan: Review of resistance & preflights Work out a circuit problem in detail

Conductivity – high for good conductors. A L Ohm’s Law: J = s E Conductivity – high for good conductors. V V = EL I = JA Observables: I/A = sV/L I = V/(L/sA) R = L sA I = V/R R = Resistance R = 1/s

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 To make R big, make L long or A small R = L sA To make R small, make L short or A big Battery is like a pump

1 CheckPoint: Two Resistors 2 Same current through both resistors Compare voltages across resistors

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?

Circuit E is conservative force  go completely around circuit Vf = Vo b c R1 E is conservative force  go completely around circuit Vf = Vo VB R2 d a -IR1 V +VB -IR2 a b c d a

Resistor Summary Series Parallel Wiring Voltage Current Resistance R1 Each resistor on the same wire. Each resistor on a different wire. Wiring Different for each resistor. Vtotal = V1 + V2 Same for each resistor. Vtotal = V1 = V2 Voltage Same for each resistor Itotal = I1 = I2 Different for each resistor Itotal = I1 + I2 Current Increases Req = R1 + R2 Decreases 1/Req = 1/R1 + 1/R2 Resistance

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: I2 > I3 I2 = I3 I2 < I3

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: I1/I2=1/2 I1/I2=1/3 I1 = I2 I1/I2=2 I1/I2=3

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: V2 > V3 V2 = V3 = V V2 = V3 < V V2 < V3

CheckPoint 2 CheckPoint 3 CheckPoint 4 R1 = R2 = R3 = R V1 V2 I1 I2 Compare the current through R1 with the current through R2 I1 I2 CheckPoint 3 Compare the voltage across R2 with the voltage across R3 V2 V3 CheckPoint 4 Compare the voltage across R1 with the voltage across R2 V1 V2

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. V1 = V2 = V V1 = 1/2 V2 = V V1 = 2V2 = V V1 =1/2 V2 =1/5 V V1 =1/2 V2 = 1/2 V

Example 9.1 In the circuit shown: V = 18V, R1 = 1W, R2 = 2W, R3 = 3W, and R4 = 4W. What is V2, the voltage across R2? 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 The purpose of this Check is to jog the students minds back to when they studied work and potential energy in their intro mechanics class.

Example 9.1 R1 R2 R1 R2 V V R3 R3 R24 R4 R1 V V R1234 R234 The purpose of this Check is to jog the students minds back to when they studied work and potential energy in their intro mechanics class.

= Quick Follow-Ups What is I3 ? A) I3 = 2 A B) I3 = 3 A C) I3 = 4 A I1 = I2 + I3 Make Sense? I1 I2 I3 R1 R2 V R1 R234 a b V = 18V R1 = 1W R2 = 2W R3 = 3W R4 = 4W R24 = 6W R234 = 2W V234= 12V V2 = 4V I1234 = 6 Amps V = R3 R4 What is I3 ? A) I3 = 2 A B) I3 = 3 A C) I3 = 4 A V3 = V234 = 12V I3 = V3/R3 = 12V/3W = 4A What is I1 ? The purpose of this Check is to jog the students minds back to when they studied work and potential energy in their intro mechanics class. We know I1 = I1234 = 6 A

Electro-Motive Force (EMF), Power In Resistors Not a force!! Electro-Motive Force (EMF), Energy provided to make charges move, units of V =VI (for a battery) = I2R (for resistor)

Example 9.2 In the circuit shown: V = 18V, R1 = 1W, R2 = 2W, R3 = 3W, and R4 = 4W. How much electrical energy does the battery put into the circuit every second in the previous problem? How much electrical energy does each resistor turn into thermal energy every second? The purpose of this Check is to jog the students minds back to when they studied work and potential energy in their intro mechanics class.

Parallel and Series (with color) V R1 R2 R4 R3 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.