General Physics (PHY 2140) Lecture 5 Electrodynamics Electric current temperature variation of resistance electrical energy and power Direct current circuits emf resistors in series http://www.physics.wayne.edu/~alan/2140Website/Main.htm Chapter 17-18 02/27/20 1 Department of Physics and Astronomy announces the Spring-Summer 2007 opening of The Physics Resource Center on Monday, May 21 in Room 172 of Physics Research Building. Hours of operation: Monday and Tuesday, Wednesday and Thursday Friday, Saturday and Sunday 10:00 AM to 5:00 PM 10:00 AM to 4:00 PM Closed Undergraduate students taking PHY1020, PHY2130, PHY2140, PHY2170/2175 and

PHY2180/2185 will be able to get assistance in this Center with their homework, labwork and other issues related to their physics course. The Center will be open: 02/27/20 Monday, May 21 to Thursday, August 2, 2007. 2 Having trouble with Physics??? Come to Supplemental Instruction (SI) Its free, helpful, and has been proven to work! Mondays: pm @ Rm. 37 State Hall Tuesdays: pm @ Rm. 27 State Hall Wednesdays: pm @ Rm. 37 State Hall Fridays: pm @ Rm. 37 State Hall If these times are inconvenient for you, email or call or come visit the: Academic success center @ 1600 UGL (313) 577-3165 www.success.wayne.edu 02/27/20

3 Exam 1 this Wednesday 5/23 12-14 questions You must show your work for credit. Closed book. You may bring an 8 x 11 inch page of notes. Bring a calculator and a pen/pencil (I dont have extras). 02/27/20 4 Suggested Course Sequence FRESHMAN YEAR Fall Physics 2130/2131 or 2170/2171 Mathematics 1800 English (BC) UGE 1000 General Education Req. Winter JUNIOR YEAR Fall Physics 5340/41: Optics Chemistry 2220/2230 or 2280/2290 Biology Elective College Foreign Lang. II

Winter Physics 5620: Electronics Physics 6Z00: Biomedical Seminar# Physics 2140/2141 or 2180/2181 Elective College Foreign Lang. III Chemistry 1220/1230 Mathematics 2010 English (IC) SENIOR YEAR Fall SOPHOMORE YEAR Fall Physics 3X00: Application of Mathematics in Biomed. Chemistry 1240/50 Mathematics 2020 Biology 1500 Winter Physics 4X00: Introduction to Biomedical Physics Biology 1510 College Foreign Lang. I General Education Req.

02/27/20 New Degree Program in BIOMEDICAL PHYSICS College Group Req. Physics 6X00: Biological Physics Elective Elective General Education Req. Winter Physics/Radiology 6Y00: Physics in Medicine Physics 6W00: Biomedical Research# College Group Req. General Education Req. # These will also be offered in the summer For more info, please contact Prof. Peter Hoffmann at [email protected] 5 Lightning Review 1 Q2 1 U QV CV 2 2

2C 2 Last lecture: 1. Capacitance and capacitors Capacitors with dielectrics (C if ) 2. Current and resistance Current and drift speed Resistance and Ohms law I is proportional to V Resistivity material property Q I t I nqvd A A C 0 , C C0

d V IR RA l Review Problem: Consider two resistors wired one after another. If there is an electric current moving through the combination, the current in the second resistor is a. equal to b. half c. smaller, but not necessarily half the current through the first resistor. 02/27/20 I a R1 b R2 c 6 17.5 Resistivity - Example (a) Calculate the resistance per unit length of a 22-gauge nichrome wire of radius 0.321 m.

Cross section: 2 3 2 A r 0.32110 m 3.24 10 7 m2 Resistivity (Table): 1.5 x 10 m. 6 R 1.5 10 m Resistance/unit length: 4.6 m 7 2 l A 3.24 10 m

02/27/20 7 17.5 Resistivity - Example (b) If a potential difference of 10.0 V is maintained across a 1.0-m length of the nichrome wire, what is the current? V 10.0V I 2.2 A R 4.6 02/27/20 8 17.6 Temperature Variation of Resistance - Intro The resistivity of a metal depends on many (environmental) factors. The most important factor is the temperature. For most metals, the resistivity increases with increasing temperature. The increased resistivity arises because of larger friction caused by the more violent motion of the atoms of the metal.

02/27/20 9 For most metals, resistivity increases approx. linearly with temperature. o 1 T To T Metallic Conductor is the resistivity at temperature T (measured in Celsius). is the reference resistivity at the reference temperature T (usually taken to be 20 oC). is a parameter called temperature coefficient of resistivity. For a conductor with fixed cross section. R Ro 1 T To 02/27/20 T

Superconductor 10 17.6 Temperature Variation of Resistance Example Platinum Resistance Thermometer A resistance thermometer, which measures temperature by measuring the change in the resistance of a conductor, is made of platinum and has a resistance of 50.0 at 20oC. When the device is immersed in a vessel containing melting indium, its resistance increases to 76.8 . Find the melting point of Indium. Solution: Using =3.92x10-3(oC)-1 from table 17.1. 02/27/20 11 Platinum Resistance Thermometer A resistance thermometer, which measures temperature by measuring the change in the resistance of a conductor, is made of platinum and has a resistance of 50.0 at 20oC. When the device is immersed in a vessel containing melting indium, its resistance increases to 76.8 . Find the melting point of Indium. R Ro 1 T To Solution: Using =3.92x10-3(oC)-1 from table 17.1. Ro=50.0 . To=20oC.

R=76.8 . R Ro 76.8 50.0 T To Ro 3.92 10 3 o C 1 50.0 137o C o T 157 C 02/27/20 12 17.7 Superconductivity 1911: H. K. Onnes, who had figured out how to make liquid helium, used it to cool mercury to 4.2 K and looked at its resistance: At low temperatures the resistance of some metals0, measured to be less than 10-16conductor (i.e., <10-24 m)! Current can flow, even if E=0.

Current in superconducting rings can flow for years with no decrease! 1957: Bardeen (UIUC!), Cooper, and Schrieffer (BCS) publish theoretical explanation, for which they get the Nobel prize in 1972. It was Bardeens second Nobel prize (1st: 1956 transistor) 02/27/20 13 17.8 Electrical energy and power In any circuit, battery is used to induce electrical current chemical energy of the battery is transformed into kinetic energy of mobile charge carriers (electrical energy gain) Any device that possesses resistance (resistor) present in the circuit will transform electrical energy into heat kinetic energy of charge carriers is transformed into heat via collisions with atoms in a conductor (electrical energy loss) C D + -

I B 02/27/20 V = IR A 14 Electrical energy Consider circuit on the right in detail AB: charge gains electrical energy form the battery E Q V (battery looses chemical energy) CD: electrical energy lost (transferred into heat) Back to A: same potential energy (zero) as before Gained electrical energy = lost electrical energy on the resistor 02/27/20 B A

C D 15 Power Compute rate of energy loss (power dissipated on the resistor) E Q P V I V t t Use Ohms law P I V I 2 V R 2 R

Units of power: SI: watt delivered energy: kilowatt-hours 02/27/20 1 kWh 103W 3600 s 3.60 106 J 16 Example Power Transmission line A high-voltage transmission line with resistance of 0.31 /km carries 1000A , starting at 700 kV, for a distance of 160 km. What is the power loss due to resistance in the wire? Given: V=700000 V =0.31 /km L=160 km I=1000 A Observations: 1. Given resistance/length, compute total resistance 2. Given resistance and current, compute power loss R L 0.31 km 160 km 49.6 Now compute power

Find: P=? 02/27/20 2 P I R 1000 A 2 49.6 49.6 106 W 17 Mini-quiz Why do the old light bulbs usually fail just after you turn them on? When the light bulb is off, its filament is cold, and its resistance is R0. Once the switch it thrown, current passes through the filament heating it up, thus increasing the resistance, R R 1 T T o o

This leads to decreased amount of power delivered to the light bulb, as P V 2 / R Thus, there is a power spike just after the switch is thrown, which burns the light bulb. 02/27/20 18 Chapter 18: Direct Current Circuits 02/27/20 19 Introduction: elements of electrical circuits A branch: A branch is a single electrical element or device (resistor, etc.).

A circuit with 5 branches. A junction: A junction (or node) is a connection point between two or more branches. A circuit with 3 nodes. If we start at any point in a circuit (node), proceed through connected electric devices back to the point (node) from which we started, without crossing a node more than one time, we form a closed-path (or loop). 02/27/20 20 18.1 Sources of EMF Steady current (constant in magnitude and direction) requires a complete circuit path cannot consist only of resistances: cannot have only potential drops in direction of current flow Electromotive Force (EMF) provides increase in potential E converts some external form of energy into electrical energy Single emf and a single resistor: emf can be thought of as a charge pump V = IR

I + - V = IR = E E 02/27/20 21 18.1 Sources of EMF (continued) Important note: in our complete circuit, conservation of energy requires that as we travel around the circuit we should encounter a number of voltage drops and increases so that we get back to the same potential we started with! V = IR I + E 02/27/20 V = IR = E

Start with 0V here and move clockwise 22 EMF Each real battery has some internal resistance AB: potential increases by E, the source of EMF, then decreases by Ir (because of the internal resistance) Thus, terminal voltage on the battery V is V E Ir B C r R E A D Note: E is the same as the

terminal voltage when the current is zero (open circuit) 02/27/20 23 EMF (continued) Now add a load resistance R Since it is connected by a conducting wire to the battery terminal voltage is the same as the potential difference across the load resistance V E Ir IR, or E Ir IR Thus, the current in the circuit is E I Rr 02/27/20 B C r R

E A D Power output: I E I 2 r I 2 R Note: well assume r negligible unless otherwise is stated 24 Measurements in electrical circuits Voltmeters measure Potential Difference (or voltage) across a device by being placed in parallel with the device. V Ammeters measure current through a device by being placed in series with the device. A 02/27/20 25 Direct Current Circuits Two Basic Principles: Conservation of Charge

Conservation of Energy a I Resistance Networks Vab IReq Vab Req I 02/27/20 Req b 26 18.2 Resistors in series A v + +_ v

2 R 2 _ B 1. Because of the charge conservation, all charges going through the resistor R2 will also go through resistor R1. Thus, currents in R1 and R2 are the same, v I1 I 2 I + Ii 1 R 1 _ 1

C 2. Because of the energy conservation, total potential drop (between A and C) equals to the sum of potential drops between A and B and B and C, V IR1 IR2 By definition, V IReq Thus, Req would be V IR1 IR2 Req R1 R2 I I Req R1 R2 02/27/20 27 Resistors in series: notes Analogous formula is true for any number of resistors,

Req R1 R2 R3 ... (series combination) It follows that the equivalent resistance of a series combination of resistors is greater than any of the individual resistors. 02/27/20 28 Resistors in series: example In the electrical circuit below, find voltage across the resistor R1 in terms of the resistances R1, R2 and potential difference between the batterys terminals V. Energy conservation implies: A v +_ + v 2 R

2 _ B with + Ii 1 R 1 _ v 1 C Then, V V1 V2 V1 IR1 and V2 IR2 V V I R1 R2 , so I R1 R2

Thus, V1 V R1 R1 R2 This circuit is known as voltage divider. 02/27/20 29 Resistors in series Conservation of Charge I = I1 = I2 = I3 Conservation of Energy Vab = V1 + V2 + V3 I a R1 V1=I1R1 V V V V Req ab 1 2 3 I I

V1 V2 V3 V1 V2 V3 I I I I1 I 2 I 3 R2 V2=I2R2 R3 V3=I3R3 Req R1 R2 R3 b Voltage Divider: 02/27/20 V1 R1 Vab Req 30 Resistors in parallel Conservation of Charge R1 I = I 1 + I2 + I 3 V1=I1R1 Conservation of Energy Vab = V1 = V2 = V3

a R2 V2=I2R2 I R3 V3=I3R3 b 1 I I I I 1 2 3 Req Vab Vab I1 I 2 I 3 I1 I 2 I 3 Vab Vab Vab V1 V2 V3 1 1 1 1 Req R1 R2 R3 Current Divider: 02/27/20 I1 Req I

R1 31 Example: Determine the equivalent resistance of the circuit as shown. Determine the voltage across and current through each resistor. Determine the power dissipated in each resistor Determine the power delivered by the battery E=18V + R1=4 R2=3 02/27/20 R3=6 32