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Electric Current An Analogy – Water Flow in a Pipe H20 gallons/minute Individual molecules are bouncing around with speeds of km/s! “Flow Rate” is the NET amount of water passing through a surface per unit time 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 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. The charges may be negative; This is the normal case for metallic conductors. The Direction of the Electric “Current” is given by the “flow” of positive charge dQ I= dt Inside a Conductor there are LOTS of charges (There may be ~1024 electrons per cm3) Area A Current I vd is “drift velocity” r vd n = # of charges q per m3 Total Current through area A is given by I = nqvd A Current per unit area is given by I J = = nqvd A J can vary in magnitude and direction in Space r r J = nqvd Vector Current Density For many materials, the local current density is proportional to the local electric field E ρ= J or r J= v E ρ ρ is known as the Resistivity of a material 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 “Non-Ohmic” materials. Many extremely important semi-conductor devices are non-ohmic. V E= L r v E = ρJ Ohm’s Law Uniform E Field What is the total Current through this object? I = JA I= E ρ A V A Lρ Lρ V= I A I= Collect all the terms that describe the object and call them “R” the: RESISTANCE V = IR Usual Statement of Ohm’s Law 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…) Circuits Direct Current – “DC” • In a DC Circuit ALL quantities (Voltage, 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=0 V Current can flow in continuous loop BUT If Resistance is NOT ZERO, We require something to keep current flowing, “ELECTRO MOTIVE FORCE” ε Continue our analogy with flowing water 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 “electro-motive 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! Inside the “Ideal EMF” r A Non Electrostatic Force Fnacts on the the charges inside the EMF. This cause the charges to ber displaces and leads to a electrostatic force Fe which “balances” the non-electrostatic force. A “resistive” path Potential difference between ends of resistive path: V =ε V = IR } ε = IR Symbols for Circuit elements Ideal conductor - generally assume that that R=0 Ideal conductor - generally assume that that R=0 Ideal EMF NOTE – device is asymmetric Ideal Resistor EMF with internal resistance Ideal Voltmeter - 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 Open Circuit EMF – Y&F Conceptual Example 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 Vab = Vac + Vcb Vab = IR + Vcb Vab = 0 + Vcb Vab = ε = 12V Voltmeter reads V=12 volt Ammeter reads A= 0 amperes Open Circuit EMF – Y&F Conceptual Example 25.2 = c Electrically First Determine the Current: V = IRtotal V = I (r + R) I 12V I= = = 2A ( r + R ) 6Ω Next Determine the Votage: Vab = Vcb − Vac Vab = ε − Ir Vab = 12v − ( 2 A)( 2Ω) Vab = 8V Important Suggestion for doing problems: First completely solve the problem algebraically… Then substitute numerical quantities to determine the numerical answer Electrostatic Potential through a complete circuit FIGURE 25.20 If I go around the circuit and come back to the same point, THE VOLTAGE MUST BE THE SAME! Power in Electric Circuits Power is defined as Energy (Work) per Unit Time dW = VabdQ dQ dW = Vab dt dt dW = Vab I dt For Pure Resistance dW P= = IV dt V2 2 P=I R= R but V = IR The sign of the power is important dW > 0 Power added to system Changes chemical energy to electrical energy and adds it to the energy in the circuit dW < 0 Power removed from system Changes electrical energy to heat and removes it from the circuit End of Chapter 25 You are responsible for the material covered in T&F Sections 25.1-25.5 You are expected to: • Understand the following terms: Current, Resistivity, Resistance, EMF, Internal Resistance, Open Circuit, Complete Circuit, Ammeter, Voltmeter, Short Circuit, Power • Determine Current and Voltage in a simple circuit. • Understand how voltmeters and ammeter’s are used and how they respond. • Determine power dissipation in a simple circuit Recommended F&Y Exercises chapter 25: • 1,13,31,35,37,43,49