Current, Resistance and Electromotive Force. Young and Freedman Chapter 25


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1 Current, Resistance and Electromotive Force Young and Freedman Chapter 25
2
3 Electric Current: Analogy, water flowing in a pipe H 2 0 gallons/minute Flow Rate is the NET amount of water passing through a surface per unit time Individual molecules are bouncing around with speeds of km/s! Net water velocity is m/s I Coulombs/s Electric Current is the NET amount of charge passing through a surface per unit time Individual electrons are bouncing around with very high speed Electron drift velocity may be mm/s
4 Electric Current In a Conductor, Charges are free to move. The charges may be positive; This is usually relevant only for special cases like ions in a solution. (Holes in semiconductors act like positive charges) The charges may be negative; This is the normal case for metallic conductors. I = dq dt
5 Inside a conductor there are LOTS of charges There could be electrons /cm 2+ Area A v d is drift velocity Current I v r d n = # of charges q per m 3 Total Current through area A is given by I = nqv d A Current per unit area is given by I J = = A nqv d J can vary in magnitude and direction in Space r J = r nqv d ector Current Density
6 Conductors, in general, follow Ohm s law For many materials, the local current density is proportional to the local electric field E r E! = or J = J! ρ is known as the Resistivity of a material v A material with a linear relationship between J and E is said to follow Ohm s Law Important note: Not all material follow Ohm s Law. Most metals do follow Ohm s Law so when we speak of a metallic conductor we are implicitly assume that the material follows Ohm s Law. This is not to be confused with a perfect conductor which has zero resistivity. There are real materials called superconductors There are many important examples of NonOhmic materials. Many extremely important semiconductor devices are nonohmic.
7 Current E = L Uniform E Field v r E =! J Ohm s Law I I I = = = = JA E A! What is the total Current through this object? A L! L! I A Collect all the terms that describe the object and call them R the: RESISTANCE = IR Usual Statement of Ohm s Law
8 Resistivity and Resistance IMPORTANT: Do not confuse Resistivity with Resisitance Resistivity is a property of a type of Material (copper, steel, water, ) Resistance is a property of a particular, specific object (a car key, a piece of wire )
9 Direct Current DC Circuits In a DC Circuit ALL quantities (oltage, Current, ) are constant Consider that the circuit has been running for a long time and will continue to run longer. In a steady state system Charge can only flow in a Loop E I E=0 I= Current can flow in continuous loop BUT If Resistance is NOT ZERO, We require something to keep current flowing, ELECTRO MOTIE FORCE ε
10 Continuing with flowing water analogy: EMF In a closed water circuit because of viscosity ( fluid friction ), there must be some motive force to maintain a steady state flow of water. In a closed electrical circuit because of resistivity ( electrical friction ), there must be some electromotive force to maintain a steady state current. ε An Ideal Electromotive Force ε provides a constant voltage between two terminals No Matter How Much Current Flows!
11 Inside the Ideal EMF A Non Electrostatic Force F r n acts on the the charges inside the EMF. This cause the charges to be displaces and leads to a electrostatic force F r e which balances the nonelectrostatic force. A resistive path Potential difference between ends of resistive path: =! = IR }! = IR
12 Symbols for circuit elements Ideal conductor  generally assume that that R=0 Ideal EMF NOTE device is asymmetric Ideal Resistor EMF with internal resistance Ideal oltmeter  generally assume that that R=  No current flows through an ideal voltmeter  A Ideal Ammeter  generally assume that that R=0 Electrically, an ideal ammeter is a perfect conductor
13 Open Circuit EMF Ex 25.2 Question: What do the meters read? First simplify circuit by replacing the meters by equivalent resistors: No complete circuit means No current c = = ac + IR + = 0 + cb cb cb =! = 12 oltmeter reads =12 volt Ammeter reads A= 0 amperes
14 Open Circuit EMF Ex 25.2 Electrically c First Determine the Current: Next Determine the oltage: = IR total = I( r + R) I I = ( r + R) = cb 12 = = 2A 6! " = # " Ir ac = 12v " (2A)(2!) = 8 Important Suggestion for doing problems: First completely solve the problem algebraically Then substitute numerical quantities to determine the numerical answer
15 Electric potential through a complete circuit FIGURE If I go around the circuit and come back to the same point, THE OLTAGE MUST BE THE SAME!
16 Power in electric circuits Power is defined as Energy (Work) per Unit Time dw dw dt dw dt = = = dq dq dt I For Pure Resistance dw P = = I dt but = IR 2 2 P = I R = R The sign of the power is important dw dw > 0 < 0 Power added to system Changes chemical energy to electrical energy and adds it to the energy in the circuit Power removed from system Changes electrical energy to heat and removes it from the circuit
17 Chapter 25 Summary
18 Chapter 25 Summary cont.
19 End of Chapter 25 You are responsible for the material covered in T&F Sections You are expected to: Understand the following terms: Current, Resistivity, Resistance, EMF, Internal Resistance, Open Circuit, Complete Circuit, Ammeter, oltmeter, Short Circuit, Power Determine Current and oltage in a simple circuit. Understand how voltmeters and ammeter s are used and how they respond. Determine power dissipation in a simple circuit Recommended Y&F Exercises chapter 25: 1, 10, 11, 31, 32, 35, 36, 44, 49
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