Physics 1202: Lecture 5 Today’s Agenda Announcements: Lectures posted on: www.phys.uconn.edu/~rcote/ HW assignments, solutions etc. Office hours: Monday 2:30-3:30 Thursday 3:00-4:00 Homework #2: On Masterphysics: due this coming Friday Go to the syllabus and click on instructions to register (in textbook section). Make sure to input oyur information to google form https://www.pearsonmylabandmastering.com/northamerica/ Labs: Already begun last week 1
Today’s Topic : Policy on clicker questions 80 % of total points gives 100% Ex: if total clicker points during semester = 255 80% of 255 = 204 points If your score is 204 or more Þ cl;icker grade = 100% Score if your score is 180 Þ cl;icker grade = 88% No make-up for missed clicker questions … Policy on clicker homework Lowest homework will be dropped No extension Chapter 21: Electric current & DC-circuits Electric current Resistance and Ohm’s law Power & Resistance in series & parallel
21- Electric Current e R I = R I
Fig 27-CO These power lines transfer energy from the power company to homes and businesses. The energy is transferred at a very high voltage, possibly hundreds of thousands of volts in some cases. Despite the fact that this makes power lines very dangerous, the high voltage results in less loss of power due to resistance in the wires. (Telegraph Colour Library/FPG)
Overview Charges in motion How charges move in a conductor mechanical motion electric current How charges move in a conductor Definition of electric current
Charges in Motion Up to now we have considered fixed charges on isolated bodies motion under simple forces (e.g. a single charge moving in a constant electric field) We have also considered conductors charges are free to move we also said that E=0 inside a conductor If E=0 and there is any friction (resistance) present no charge will move!
Is there a contradiction? Charges in motion We know from experience that charges do move inside conductors - this is the definition of a conductor E E Is there a contradiction? no V1 V2 Up to now we have considered isolated conductors in equilibrium. Charge has nowhere to go except shift around on the body. Charges shift until they cancel the E field, then come to rest. Now we consider circuits in which charges can circulate if driven by a force such as a battery.
Analogy with fluids Consider a hose filled with water Need a difference of potential for fluid to flow Same is true for electric charges
Current Definition + E Consider charges moving down a conductor in which there is an electric field. If we take a cross section of the wire, over some amount of time Dt we will count a certain number of charges (or total amount of charge) DQ moving by. We define current as the ratio of these quantities, Iavg = DQ / Dt Units for I, Coulombs/Second (C/s) or Amperes (A) Note: This definition assumes the current in the direction of the positive particles, NOT in the direction of the electrons!
How charges move in a conducting material Electric force causes gradual drift of bouncing electrons down the wire in the direction of -E. Drift speed of the electrons is VERY slow compared to the speed of their bouncing motion, roughly 1 m / h ! (see example later) Good conductors are those with LOTS of mobile electrons.
How charges move in a conducting material DQ is the number of carriers in some volume times the charge on each carrier (q). Let n be the carrier density, n = # carriers / volume. The relevant volume is A * (vd Dt). Why ? So, DQ = n A vd Dt q And Iavg = DQ/Dt = n A vd q More on this later … vd = Δx/ Δt
Drift speed in a copper wire The copper wire in a typical residential building has a cross-section area of 3.31e-6 m2. If it carries a current of 10.0 A, what is the drift speed of the electrons? (Assume that each copper atom contributes one free electron to the current.) The density of copper is 8.95 g/cm3, its molar mass 63.5 g/mol. Volume of copper (1 mol): Because each copper atom contributes one free electron to the current, we have (n = #carriers/volume)
Drift speed in a copper wire, ctd. We find that the drift speed is with charge / electron q Thus
What makes charges move ? Need to create DV recall W = -DU A battery uses chemical reactions to produce a potential difference V1 V2 Fluid analogy: person lifting water causing it to flow through the paddle wheel and do work.
Electromotive “force” Electric potential difference between the terminals of a battery is called the electromotive force or emf: Remember—despite its name, the emf is an electric potential, not a force. The amount of work it takes to move a charge ΔQ from one terminal to the other is: + - e
© 2017 Pearson Education, Inc. Electric current The direction of current flow from the positive terminal to the negative one was decided before it was realized that electrons are negatively charged. Current flows around a circuit in the direction a positive charge would move; electrons move the other way. Does not matter in most circuits. © 2017 Pearson Education, Inc.
21-2: Resistance & Ohm’s Law V I R Resistance Resistance is defined to be the ratio of the applied voltage to the current passing through. UNIT: OHM = W What does it mean ? it is the a measure of the friction slowing the motion of charges Analogy with fluids
Ohm’s Law Experiments show that for many materials, including most metals, the resistance remains constant over a wide range of applied voltages or currents This statement has become known as Ohm’s Law ΔV = I R Ohm’s Law is an empirical relationship that is valid only for certain materials Materials that obey Ohm’s Law are said to be ohmic Georg Simon Ohm
Ohm's Law R I V Vary applied voltage V. Measure current I Does ratio ( V/I ) remain constant?? V I slope = R = constant
Ohm’s Law, cont An ohmic device The resistance is constant over a wide range of voltages The relationship between current and voltage is linear The slope is related to the resistance Non-ohmic materials are those whose resistance changes with voltage or current The current-voltage relationship is nonlinear A diode is a common example of a non-ohmic device
Resistivity R I V Resistance: for a ohmic device UNIT: OHM = W Is this a good definition? i.e. does the resistance belong only to the resistor? Recall the case of capacitance: (C=Q/V) depended on the geometry, not on Q or V individually Does R depend on V or I ? R is proportional to its length, L, and inversely proportional to its cross-sectional area, A ρ is the constant of proportionality and is called the resistivity of the material
Make sense? DV r I A L Increase the Length, flow of electrons impeded Increase the cross sectional Area, flow facilitated Analogy with fluids: think of the viscosity & friction Longer hose: more resistance to flow Larger/wider hose: easier to flow (less friction with walls). So, in fact, we can compute the resistance if we know a bit about the device, and YES, the property belongs only to the device ! e.g, for a copper wire, r ~ 10-8 W-m, 1mm radius, 1 m long, then R » .01W
Resistivity of subtances The difference between insulators, semiconductors, and conductors can be clearly seen in their resistivities: © 2017 Pearson Education, Inc.
Lecture 5, ACT 1 (a) I1 < I2 (b) I1 = I2 (c) I1 > I2 V Two cylindrical resistors, R1 and R2, are made of identical material. R2 has twice the length of R1 but half the radius of R1. These resistors are then connected to a battery V as shown: V I1 I2 What is the relation between I1, the current flowing in R1 , and I2 , the current flowing in R2? (a) I1 < I2 (b) I1 = I2 (c) I1 > I2
Which of the graphs represents the current I around the loop? Lecture 5, ACT 2 R e I 1 2 3 4 + - Consider a circuit consisting of a single loop containing a battery and a resistor. Which of the graphs represents the current I around the loop? x 1 2 3 4 + -
Which of the graphs represents the potential V around the loop? Lecture 5, ACT 2 addendum x 1 2 3 4 + - Which of the graphs represents the potential V around the loop?
Note on Electromotive force Provides a constant potential difference between 2 points e: “electromotive force” (emf) + - e May have an internal resistance Not “ideal” (or perfect: small loss of V) Parameterized with “internal resistance” r in series with e e R I r V Potential change in a circuit e - Ir - IR = 0
Effect of temperature E Resistivity accounts for the friction of moving charges In quantum mechanics the electron can be described as a wave. Because of this the electron will not scatter off of atoms that are perfectly in place in a crystal. Electrons will scatter off of 1. Vibrating atoms (proportional to temperature) 2. Other electrons (proportional to temperature squared) 3. Defects in the crystal (independent of temperature)
Resistivity versus Temperature In lab you measure the resistance of a light bulb filament versus temperature. You find RT. This is generally (but not always) true for metals around room temperature. temperature coefficient of resistivity For insulators R1/T. At very low temperatures atom vibrations stop. Then what does R vs T look like?? This was a major area of research 100 years ago – and still is today.
21-3: Power Battery: Stores energy chemically. When attached to a circuit, the energy is transferred to the motion of electrons. This happens at a constant potential. Battery delivers energy to a circuit. Other elements, like resistors, dissipate energy. (light, heat, etc.) Total energy delivered not always useful. How much energy does it take to light your house … well for how long? Remember definition of Power (Phys. 1201).
Power Recall that In a circuit, where the potential remains constant. Only q varies with time
Power Batteries & Resistors Energy expended What’s happening? Assert: chemical to electrical to heat Rate is: What’s happening? Assert: Charges per time Energy “drop” per charge For Resistors: Units okay?
Power What does power mean? Power delivered by a battery is the amount of work per time that can be done. i.e. drive an electric motor etc. Power dissipated by a resistor, is amount of energy per time that goes into heat, light, etc. A light bulb is basically a resistor that heats up. The brightness (intensity) of the bulb is basically the power dissipated in the resistor. A 200 W bulb is brighter than a 75 W bulb, all other things equal.
Batteries (non-ideal) Parameterized with “internal resistance” r in series with e e: “electromotive force” (emf) e R I r V = V(I=0) e - Ir = V e - Ir - IR = 0 Power delivered to the resistor R: Þ Pmax when R/r =1 !
Figure 28.3 (Example 28.2) Graph of the power delivered by a battery to a load resistor of resistance R as a function of R. The power delivered to the resistor is a maximum when the load resistance equals the internal resistance of the battery.
Lecture 5, Act 3 You buy two light bulbs at the hardware store, a 200 W bulb and a 100 W bulb. Which bulb has the larger resistance? A) 200 W bulb B) 100 W bulb C) Same
21-4: Electric Circuits e R I = R I
Devices Conductors: Purpose is to provide zero potential difference between 2 points. Electric field is never exactly zero.. All conductors have some resistivity. In ordinary circuits the conductors are chosen so that their resistance is negligible. Batteries (Voltage sources, seats of emf): Purpose is to provide a constant potential difference between 2 points. Cannot calculate the potential difference from first principles.. electrical « chemical energy conversion. Non-ideal batteries will be dealt with in terms of an "internal resistance". + - V OR
Devices R I V Resistors: Purpose is to limit current drawn in a circuit. Resistance can be calculated from knowledge of the geometry of the resistor AND the “resistivity” of the material out of which it is made. The effective resistance of series and parallel combinations of resistors will be calculated using the concepts of potential difference and current conservation (Kirchoff’s Laws). V I R Resistance Resistance is defined to be the ratio of the applied voltage to the current passing through. UNIT: OHM = W
Resistors in Series R1 The Voltage “drops”: R2 b c R1 R2 I The Voltage “drops”: a c Reffective Whenever devices are in SERIES, the current is the same through both ! This reduces the circuit to: Hence:
Another (intuitive) way... L2 L1 Consider two cylindrical resistors with lengths L1 and L2 Put them together, end to end to make a longer one...
Equivalent Resistance – Series: An Example Four resistors are replaced with their equivalent resistance
Resistors in Parallel I R1 R2 I1 I2 V I R V a d a d Þ Þ What to do? Very generally, devices in parallel have the same voltage drop But current through R1 is not I ! Call it I1. Similarly, R2 «I2. a d I R V How is I related to I 1 & I 2 ?? Current is conserved! Þ Þ
Another (intuitive) way... Consider two cylindrical resistors with cross-sectional areas A1 and A2 V R1 R2 A1 A2 Put them together, side by side … to make a “fatter” one with A=A1+A2 , Þ
Summary R1 V R2 V R1 R2 Resistors in series Resistors in parallel the current is the same in both R1 and R2 the voltage drops add Resistors in parallel the voltage drop is the same in both R1 and R2 the currents add V R1 R2
Equivalent Resistance – Complex Circuit
Recap of today’s lecture Chapter 21: Electric current & DC-circuits Electric current Resistance and Ohm’s law Power Resistance in series & parallel Office hours: Monday 2:30-3:30 Thursday 3:00-4:00 Homework #2: On Masterphysics: due this coming Friday