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Chapter 25 Current, Resistance, and Electromotive Force PowerPoint® Lectures for University Physics, Thirteenth Edition – Hugh D. Young and Roger A. Freedman Lectures by Wayne Anderson Copyright © 2012 Pearson Education Inc. Modified 2016 Scott Hildreth – Chabot College Goals for Chapter 25 • To understand current & how charges move in a conductor • To understand resistivity and conductivity • To calculate resistance of a conductor • To learn how an emf (E) causes current in a circuit • To calculate energy & power in circuits Current • Current is any motion of charge from one region to another. • Current I = dQ/dt [Amps] • E field in conductor causes charges to flow. • E field created by Potential Difference! Direction of current flow • A current can be produced by positive or negative charge flow. • Conventional current is treated as a flow of positive charges. • The moving charges in metals are electrons (see figure below). Current, drift velocity, and current density • Suppose: – n charged particles/volume – drift velocity vd – time element dt – Cross-sectional area A • dQ = q (nAvd dt) • I = dQ/dt = nqAvd (scalar) • Define current density J – J = I/A = nqvd (vector) Current, drift velocity, and current density • Example: – 18 gauge wire (diameter = 1.02 mm); Current, drift velocity, and current density • Example: – 18 gauge wire (diameter = 1.02 mm); – current 1.67 A – 200 Watt lamp – Electron density = 8.5 x 1028/m3 . • What is J and vd? Resistivity • Resistivity of material = ratio of E field in material to current density it causes: = E/J. • Large = LARGE field needed to generate small current! Resistivity • Conductivity is the reciprocal of the resistivity. • High conductivity = large current results from small E field. Resistivity and temperature • Resistivity depends on temperature. • ~ Linear R(T) = R0[1+a(T-T0)] Resistance • Resistance of conductor R = L/A [Ohms] • Potential decreases across a conductor is V = IR • Going from higher V to lower; in direction of current • V = IR (Ohm’s Law) … OR… I = V/R Resistors are color-coded for easy identification • This resistor has a resistance of 5.7 kΩ with a tolerance of ±10%. Ohmic and nonohmic resistors • Only resistor in Figure (a) below obeys Ohm’s law. Electromotive force and circuits • An electromotive force (emf) makes current flow. In spite of the name, an emf is not a force. • “EMF” is a voltage difference! • Ideal source – EMF is constant • Vab = E • For simple complete circuits, EMF “pushes” + current around from start to finish. + Electromotive force and circuits EMF in an open circuit (Battery not connected to anything) Electromotive force and circuits EMF in an complete circuit Internal resistance • Real sources of emf actually contain some internal resistance r. • The terminal voltage of an emf source is Vab = – Ir. • Terminal voltage of 12-V battery is less than 12 V when actually connected to the light bulb. Symbols for circuit diagrams Example 25.4 – OPEN circuit • EMF = 12 V; internal r = 2 Ohms (very large!!!) • Not connected to anything (yet) • What do ideal Voltmeter and Ammeter read? Source in a complete circuit • Now add a 4-Ohm resistor to the same source…. • What is total resistance? What is current? Vab? Source in a complete circuit • Now add a 4-Ohm resistor to the same source…. • Total resistance of SERIES resistors = 2 + 4 = 6 Ohms Source in a complete circuit Vab: 12V – (2A x 2W) = 8V Va’b’ = IR 2A x 4W = 8V Ideal I = 12V/6 W =2A Using voltmeters and ammeters What do Ammeters and Voltmeters do to circuits? Using voltmeters and ammeters What do Ammeters and Voltmeters do to circuits? Ammeters measure flow of current PAST a point. Ideally, they should NOT influence the current Ideally, R(ammeter) = 0! Put them IN SERIES with circuit “legs” Using voltmeters and ammeters What do Ammeters and Voltmeters do to circuits? Voltmeters measure pressure difference across (or between) points in the circuit. Ideally, they should NOT influence the current Ideally, R(voltmeter) = ! Put them in parallel! Using voltmeters and ammeters What do Ammeters and Voltmeters do to circuits? Using voltmeters and ammeters What do Ammeters and Voltmeters do to circuits? Voltmeter in Series! R(voltmeter) = No current will flow! A source with a short circuit • Without a resistor, what happens? Potential changes around a circuit • “Loop Rule”: – NET change in potential = zero for “round trip” in a circuit • Net EMF for a loop equals sum of voltage “drops” across resistors and/or other elements. Energy and power in electric circuits • Rate energy is delivered to (or extracted from) a circuit element is P = VabI. • [POWER] = [WATTS] • Power delivered to pure resistor: P = I2R = Vab2/R. Energy and power in electric circuits • Rate energy is delivered to (or extracted from) a circuit element is P = VabI. • [POWER] = [WATTS] • Power delivered to pure resistor: P = I2R = Vab2/R. Power input and output • What are rates of energy conversion and power dissipation in circuit? Power input and output • What are rates of energy conversion and power dissipation in circuit? – Battery provides EI = 12 V x 2A = 24 Watts – Energy dissipation in battery = I2r = 8 Watts – Energy dissipation in 4W resistor = 16 Watts Power in a short circuit • Short Circuit bypasses resistance, allowing charge to flow without “obstruction” Remove this! Power in a short circuit • Now power = 12 V x 6A = 72 W = I2R(internal) Theory of metallic conduction • Random motion of electrons in a conductor. PGE Rates & Meanings…. • PGE Home rates (3/16): • What’s a KWh?? PGE Rates & Meanings…. • What’s a KWh?? • Kilowatt = 1000 Watts = 1000 Joules/Second • Kilowatt-hour = 1000 Watts x 3600 seconds • = 3.6 x 106 Joules = 3.6 MegaJoules • = 3.6 MJ • How much energy do I use? • 100W light bulb 5 hours at night to study physics? • 0.1 KW x 5 hours = 0.5 KWh @ $.18/KWh • Only 9 CENTS!!! (See!! Study physics more!) What do we use on average in the US? ~ 911 KWh/residence/month2 (electricity) ~ 12,000 KWh/year ~ 80K – 90K KWh (80- 90 MWh) of energy from all sources per person per year1 Sources: 1 US Department of Energy [Internet]. How much electricity does an American home use? 2012 Oct 3. http://www.eia.gov/tools/faqs/faq.cfm?id=97&t=3 2 Energy in the United States. (2016, March 7). In Wikipedia, The Free Encyclopedia. Retrieved March 7, 2016, from https://en.wikipedia.org/w/index.php?title=Energy_in_the_United_States&oldid=708828662