lecture12_current_072711

# lecture12_current_072711 - Physics 142 7/27/2011 Midterm 1...

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Unformatted text preview: Physics 142 7/27/2011 Midterm 1 Raw Raw scores out of 50 – Average (mean): ~30 – Median: ~30 Chance Chance to correct two problems Additionally Additionally some curve (TBD) – Avg in low B range Physics 142 Summer 2011 Midterm Corrections and HW HWs HWs 5 & 6 will be due next Tuesday/Wednesday (MP/written) Midterm Midterm corrections will be due Friday – Correct 2 exam problems » Print out fresh copy of the page from ELMS » Answer to the best of your ability (you can ask Anton or me for help but not others) » Give short explanation of how your thinking changed between the exam version and your new answer – turn in in lecture Friday – For those problems get the average of your old and new scores Physics 142 Summer 2011 How to think about current? Unless Unless we are going to be materials science physicists, we don’t really need to understand the quantum view of conduction. Instead, Instead, we construct a bunch analogies that have some of the correct features. – water flow – air flow These These help us make sense of the fundamental laws that govern current flow. Physics 142 Summer 2011 Dr. Nick Cummings 1 Physics 142 7/27/2011 The fluid flow model Key Key concept: Pressure Recall: Recall: 1 2 3 4 – Pressure is like a tension but in 3D. – It pushes in all directions at once, so it has no direction. – Forces due to pressure occur when you only let it push on one side of an area. Then r r F = PA Physics 142 Summer 2011 Viscous Drag A fluid flowing in a pipe doesn’t slip through the fluid pipe frictionlessly. The The fluid sticks to the walls moves faster at the middle of the pipe than at the edges. As a result, it has to “slide over itself” (shear). There There is friction between layers of fluid moving at different speeds that creates a viscous drag force, trying to reduce the sliding. The The drag is proportional to the speed and the length of pipe. Fdrag = 8πµLv Physics 142 Summer 2011 Implication: Pressure drop If If we have a fluid moving at a constant rate and there is drag, N2 tells us there must be another force to balance the drag. The The internal pressure in the fluid must drop in the direction of the flow to balance drag. Drag force Flow in Flow out Pressure force Pressure force upstreamPhysics 142 Summer 2011 downstream Dr. Nick Cummings 2 Physics 142 7/27/2011 Waterflow Equations Matter Matter is moving: describe how much J= ∆Volume ∆t J= Av What What keeps the mass moving, even though there is resistance? ma = Fp − cv a=0 ⇒ v= Fp c Physics 142 Summer 2011 Quantifying current Consider Consider a wire containing movable current carriers (electrons). Define Define the electric current as rate at which charge moves past a surface. v n I= ∆q ∆t A v ∆t The The unit of current is the Ampere (= 1C/s) Physics 142 Summer 2011 How Much Current? If If there is a density of electrons n per unit volume and they are moving with a velocity v, then how many cross the surface in a time ∆t? L = v ∆t Volume LA Volume = LA N = n (LA) = nAv ∆t (LA) I = qnAv qnAv v n A ∆x = v ∆ t Physics 142 Summer 2011 Dr. Nick Cummings 3 Physics 142 7/27/2011 Charge Flow Equations ∆q ∆t Charge Charge is moving: describe how much I= How How does this relate to the individual charges? I=qnAv What What pushes the charges through resistance? ma = Fe − bv a=0 ⇒ v= Fe b Physics 142 Summer 2011 Current Density Another Another way to express the flow of charge is How How does this relate to the individual charges? J= I A J= q n v The The current density tells us the amount of current flowing per cross sectional area Physics 142 Summer 2011 A set of sodium ions (Na+) are flowing across an area A at a velocity v. If the speed of the ions doubles, the current across A 0% 1. 0% 2. 0% 3. 0% 4. 0% 5. v n A v ⊗t Doubles Halves Stays the same Changes in some other way There is not enough information to decide. Physics 142 Summer 2011 Dr. Nick Cummings 4 Physics 142 7/27/2011 A set of sodium ions (Na+) are flowing across an area A at a velocity v. If the area the ions v are crossing doubles (spreading out the same ions), the current across A 0% 1. 0% 2. 0% 3. 0% 4. 0% 5. n A Doubles v ⊗t Halves Stays the same Changes in some other way There is not enough information to decide. Physics 142 Summer 2011 Overcoming the drag Consider Consider an electron moving in a conductor with a uniform electric field To To push the electrons through the drag we need a force. ∆V ma = F net 0 = qE − bv qE = bv d Physics 142 Summer 2011 Rearrange Express Express E in terms of ∆V (easier to measure) (easier Express Express v in terms of I (ditto). ∆V d I I = qnAv ⇒ v = qnA ∆V = Ed So qE = bv ⇒ ⇒ E= q∆V bI = d qnA bd ∆V = I 2 ≡ IR q nA Physics 142 Summer 2011 Dr. Nick Cummings 5 Physics 142 7/27/2011 Ohm’s Law Current Current proportional to velocity Due Due to resistance, drag force proportional to velocity. Electric Electric force proportional to “electric pressure drop” = “electric PE” Therefore, Therefore, current proportional to “electric PE” ∆V = IR Physics 142 Summer 2011 Ohm’s “Law” This This is called a “law” for historical reasons This This is came from assuming a particular sort of “drag” on the electrons – Describes “ohmic resistors’ “ohmic ∆V = IR You You could have other sorts of drag – non-Ohmic resistors non- Still, Still, Ohms law is approximately correct for many situations, so it’s very useful Physics 142 Summer 2011 Fluid vs. Electricity Fluid: Fluid: 8πµL ∆P = J 2 A Electricity: Electricity: Resistance to flow bd ∆V = IR = I 2 q nA – R is the resistance to the flow of current – Goes up with d and down with A, like for a fluid Physics 142 Summer 2011 Dr. Nick Cummings 6 Physics 142 7/27/2011 Electric circuit elements Batteries Batteries —devices that maintain a constant electrical pressure difference across their terminals (like a water pump that raises water to a certain height). Resistance Resistance —devices that have significant drag and oppose current. Pressure will drop across them. Wires — have very little resistance. Wires We can ignore the drag in them (mostly – as long as there are other resistances present). Physics 142 Summer 2011 Analogy: The rope model Since Since like charges repel each other so strongly, there can’t be a buildup of charge anywhere in the circuit (unless we make a special arrangement -- see capacitance). So So moving charges push other movable charges in front of them. The electrons move like links in a chain or rope. Physics 142 Summer 2011 Properties of rope analogy In In a simple loop, the rope keeps moving around. A battery is like a person holding the rope and battery pulling it, causing a tension throughout the rope. A resistor is like a person squeezing the rope, resistor having it pulled through her hands. The friction generates heat. The The more people are squeezing, the slower the rope goes, even if the battery pulls with the same tension. Physics 142 Summer 2011 Dr. Nick Cummings 7 Physics 142 7/27/2011 Analogy: Water flow The The rope analogy fails because electrons can go either way at a junction. A current can split in a way a rope cannot. Water Water flow is a useful analogy because water – can divide – is conserved and cannot be compressed (for practical purposes). Physics 142 Summer 2011 Water Model pump and storage bin (battery) water wheel (bulb) sluices (wires) Physics 142 Summer 2011 The current rule The The most useful result that carries over from the water flow analogy to the flow of electric current is: Kirchhoff’s Kirchhoff’s current rule: – The total amount of current flowing into any point in a network equals the amount flowing out (there is no significant build-up of charge buildanywhere). Physics 142 Summer 2011 Dr. Nick Cummings 8 Physics 142 7/27/2011 The Potential Rule The The water flow and nail board analogy uses gravity instead of electric force. It has the following property: Gravity Gravity potential rule: – Whenever you walk around a loop, however far you went up is equal to however far you went down. (You wind up at the same place.) Electric Electric potential for electric forces is analogous to height (times g) for gravitational forces. Kirchhoff’s Kirchhoff’s potential rule: – Around any loop the sum of the potential drops = the sum of the potential rises. Physics 142 Summer 2011 Kirchoff’s Rules Flow Flow Rule – The total amount of current flowing into any point in a network equals the amount flowing out (no significant build-up of charge anywhere). build- Potential Potential Rule – Following around any loop in an electrical network the potential has to come back to the same value (sum of drops = sum of rises). Ohm’s Ohm’s Rule – When a current I passes through a resistance R, there is a R, there voltage drop across the resistor of an amount ∆V = IR Physics 142 Summer 2011 Very useful heuristic The The Constant Potential Trick – Along any part of a circuit with 0 resistance, then ∆V = 0, i.e., the voltage is constant. 0, Usually Usually our circuits will have resistors with big R values and wires with small R that can be neglected – Two points attached by a wire can be considered to have the same potential Physics 142 Summer 2011 Dr. Nick Cummings 9 Physics 142 7/27/2011 Electric Power Dissipation We We can figure out the energy needed to push the electrons through the material against the resistance using the WE theorem. P = rate of doing work (using energy) = ∆W ∆t = (number of charges moved) × (force) × (distance moved in a time ∆t ) P= ( nAL)(qE )(v∆t ) ∆V = (nAL)qv = (nAqv)∆V = I∆V L ∆t Physics 142 Summer 2011 Units of power Since Since the units of work (energy) is the Joule, the unit of power is the Joule/second. – 1 Watt = 1 Joule/second (definition) Our Our analysis shows that current x voltage = power. 1 Watt = 1 Ampere x 1 Volt Watt Physics 142 Summer 2011 US Terminology Current Current is sometimes referred to as “amperage” In In the US electrical energy is often measured in kilowatt-hours kilowatt– Energy = (power) x (time) J 1 kw ⋅ hr = 1000 ⋅ 3600 s = 3.6 MJ s Physics 142 Summer 2011 Dr. Nick Cummings 10 ...
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## This note was uploaded on 10/03/2011 for the course BSCI 410 taught by Professor Staff during the Spring '08 term at Maryland.

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