General Physics (PHY 2140) Lecture 9 Electrodynamics Electric current temperature variation of resistance electrical energy and power http://www.physics.wayne.edu/~apetrov/PHY2140/ Chapter 17-18 11/10/2018

The Physics Resource Center Room 172 of Physics Research Building. Department of Physics and Astronomy announces the Fall 2003 opening of The Physics Resource Center on Monday, September 22 in Room 172 of Physics Research Building. Hours of operation: Mondays, Tuesdays, Wednesdays 11 AM to 6 PM Thursdays and Fridays 11 AM to 3 PM Undergraduate students taking PHY2130-2140 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: Monday, September 22 to Wednesday, December 10, 2003. 11/10/2018

Lightning Review R1 R2 Last lecture: Current and resistance Current and drift speed Resistance and Ohm’s law I is proportional to V Resistivity material property 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. a b c R1 R2 I 11/10/2018

17.4 Resistivity - Example (a) Calculate the resistance per unit length of a 22-gauge nichrome wire of radius 0.321 m. Cross section: Resistivity (Table): 1.5 x 10-6 Wm. Resistance/unit length: 11/10/2018

17.4 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? 11/10/2018

17.4 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. 11/10/2018

r is the resistivity at temperature T (measured in Celsius). For most metals, resistivity increases approx. linearly with temperature. r T Metallic Conductor r is the resistivity at temperature T (measured in Celsius). ro is the reference resistivity at the reference temperature To (usually taken to be 20 oC). a is a parameter called temperature coefficient of resistivity. For a conductor with fixed cross section. r T Superconductor 11/10/2018

17.5 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 W at 20oC. When the device is immersed in a vessel containing melting indium, its resistance increases to 76.8 W. Find the melting point of Indium. Solution: Using a=3.92x10-3(oC)-1 from table 17.1. 11/10/2018

Using a=3.92x10-3(oC)-1 from table 17.1. Ro=50.0 W. To=20oC. R=76.8 W. 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 W at 20oC. When the device is immersed in a vessel containing melting indium, its resistance increases to 76.8 W. Find the melting point of Indium. Solution: Using a=3.92x10-3(oC)-1 from table 17.1. Ro=50.0 W. To=20oC. R=76.8 W. 11/10/2018

Appendix: 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 metals0, measured to be less than 10-16•ρconductor (i.e., ρ<10-24 Ωm)! 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 Bardeen’s second Nobel prize (1956 – transistor) 11/10/2018

17.7 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) I V = IR + - D C B A 11/10/2018

Electrical energy Consider circuit on the right in detail AB: charge gains electrical energy form the battery (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 C B A D 11/10/2018

Power Compute rate of energy loss (power dissipated on the resistor) Use Ohm’s law Units of power: SI: watt delivered energy: kilowatt-hours 11/10/2018

Example Power Transmission line A high-voltage transmission line with resistance of 0.31 W/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 r=0.31 W/km L=160 km I=1000 A Find: P=? Observations: Given resistance/length, compute total resistance Given resistance and current, compute power loss Now compute power 11/10/2018

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, so its resistance is large. Once the switch it thrown, current passes through the filament heating it up, thus increasing the resistance, This leads to decreased amount of power delivered to the light bulb, as Thus, there is a power spike just after the switch is thrown, which burns the light bulb. Resume: electrical devices are better be turned off if there is a power loss 11/10/2018

Direct Current Circuits 11/10/2018

18.1 Sources of EMF Steady current (constant in magnitude and direction) requires a complete circuit path cannot be only resistance cannot be 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” I V = IR E + - V = IR = E 11/10/2018

EMF Each real battery has some internal resistance AB: potential increases by E on the source of EMF, then decreases by Ir (because of the internal resistance) Thus, terminal voltage on the battery DV is Note: E is the same as the terminal voltage when the current is zero (open circuit) B C r R E A D 11/10/2018

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 Thus, the current in the circuit is B C r R E A D Power output: 11/10/2018 Note: we’ll assume r negligible unless otherwise is stated

Measurements 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 11/10/2018

Direct Current Circuits Two Basic Principles: Conservation of Charge Conservation of Energy Resistance Networks Req I a b 11/10/2018

Conservation of Charge I = I1 = I2 = I3 Conservation of Energy Resistors in series Conservation of Charge I = I1 = I2 = I3 Conservation of Energy Vab = V1 + V2 + V3 a b I R1 V1=I1R1 R2 V2=I2R2 R3 V3=I3R3 Voltage Divider: 11/10/2018

Conservation of Charge I = I1 + I2 + I3 Conservation of Energy Resistors in parallel Conservation of Charge I = I1 + I2 + I3 Conservation of Energy Vab = V1 = V2 = V3 a R1 V1=I1R1 R2 V2=I2R2 R3 V3=I3R3 b Current Divider: 11/10/2018

R1=4W E=18V R3=6W R2=3W 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 R1=4W E=18V R2=3W R3=6W 11/10/2018