EE40Lecture 2Venkat AnantharamThe Ideal Basic Circuit ElementElectric PowerPassive Sign ConventionSign Convention for PowerElectrical ResistanceCurrent vs. Voltage (I-V) CharacteristicElectrical ConductanceElectrical SourcesIdeal Voltage SourceI-V Characteristic of Ideal Voltage SourceIdeal Current SourceI-V Characteristic of Ideal Current SourceSlide 1EE40 Spring 08 Venkat AnantharamEE40Lecture 2Venkat Anantharam1/25/08 Reading: Chap. 1Slide 2EE40 Spring 08 Venkat AnantharamThe Ideal Basic Circuit Elementi+v_• Polarity reference for voltage can beindicated by plus and minus signs• Reference direction for the currentis indicated by an arrowAttributes:• Two terminals (points of connection)• Mathematically described in terms of current and/or voltage• Cannot be subdivided into other elementsSlide 3EE40 Spring 08 Venkat AnantharamElectric Power• Definition: transfer of energy per unit time• Symbol: p• Units: Joules per second ≡ Watts (W)p = dw/dt = (dw/dq)(dq/dt) = vi• Concept:As a positive charge q moves through a drop in voltage v, it loses energy energy change = qv rate is proportional to # charges/secJames Watt1736 - 1819Slide 4EE40 Spring 08 Venkat AnantharamPassive Sign Convention+v_ip = vi• If p > 0, power is being delivered to the box. – The element is a passive element.• If p < 0, power is being generated from the box.– The element is an active element. • How can a circuit element absorb power?– By converting electrical energy into heat (resistors in toasters), light (light bulbs), or acoustic energy (speakers); by storing energy (charging a battery).Slide 5EE40 Spring 08 Venkat AnantharamSign Convention for PowerPassive sign conventionActive sign convention• If p > 0, power is being delivered to the box. • If p < 0, power is being extracted from the box.+v_i_v+p = vi p = -vii i i+v__v+Irrespective of the sign conventionSlide 6EE40 Spring 08 Venkat AnantharamElectrical Resistance• Resistance: the ratio of voltage drop and current. The circuit element used to model this behavior is the resistor.Circuit symbol:Units: Volts per Ampere ≡ ohms (Ω) • The current flowing in the resistor is proportional to the voltage across the resistor:v = i Rwhere v = voltage (V), i = current (A), and R = resistance (Ω)R(Ohm’s Law)Georg Simon Ohm1789-1854Slide 7EE40 Spring 08 Venkat AnantharamCurrent vs. Voltage (I-V) Characteristic+v_iivWhat is the I-V characteristic for an ideal resistor?The slope must be positive and the characteristic must go through the origin.Slide 8EE40 Spring 08 Venkat AnantharamElectrical Conductance• Conductance is the reciprocal of resistance.Symbol: GUnits: siemens (S) or mhos ( )Example:Consider an 8 Ω resistor. What is its conductance?ΩWerner von Siemens 1816-1892Slide 9EE40 Spring 08 Venkat AnantharamElectrical Sources•An electrical source is a device that is capable of converting non-electric energy to electric energy and vice versa.Examples:– battery: chemical electric– dynamo (generator/motor): mechanical electric(Ex. gasoline-powered generator, Bonneville dam)ÆElectrical sources can either deliver or absorb powerSlide 10EE40 Spring 08 Venkat AnantharamIdeal Voltage Source• Circuit element that maintains a prescribed voltage across its terminals, regardless of the current flowing in those terminals.– Voltage is known, but current is determined by the circuit to which the source is connected.• The voltage can be either independent ordependent on a voltage or current elsewhere in the circuit, and can be constant or time-varying.Device symbols:+_+_vs=µ vx+_vsvs=ρ ixindependent current-controlledvoltage-controlledSlide 11EE40 Spring 08 Venkat AnantharamI-V Characteristic of Ideal Voltage Sourceii1. Plot the I-V characteristic for vs> 0. For what values of i does the source absorb power? For what values of i does the source release power?2. Repeat (1) for vs< 0.3. What is the I-V characteristic for an ideal wire?+_vs+Vab_abvVs>0 Æ i<0 release power; i>0 absorb poweri=0Vs>0Slide 12EE40 Spring 08 Venkat AnantharamIdeal Current Source• Circuit element that maintains a prescribed current through its terminals, regardless of the voltage across those terminals.– Current is known, but voltage is determined by the circuit to which the source is connected.• The current can be either independent or dependent on a voltage or current elsewhere in the circuit, and can be constant or time-varying.Device symbols:isis=α vxis=β ixindependent current-controlledvoltage-controlledSlide 13EE40 Spring 08 Venkat AnantharamI-V Characteristic of Ideal Current Sourceii1. Plot the I-V characteristic for is> 0. For what values of v does the source absorb power? For what values of v does the source release power?+v_isV>0 absorb power; V<0 release
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