EE201 Lecture 2 P 1 Voltage Sources Power Voltage Charged metal plates with E field A B E d Consider a positive charge q placed at point A at t 0 with no kinetic energy What happens Charge accelerates toward B with increasing kinetic energy Since total energy is conserved the kinetic energy at B equals the change in potential energy from A to B Energy is converted from one form to another EE201 Lecture 2 P 2 Potential energy difference between A and B Kinetic energy at B Kinetic energy at B q The proportionality constant in Eqn above is defined as the potential difference or voltage between A and B Energy q V Voltage is not energy Unit of voltage or potential difference Volt V If 1 Joule of energy is converted from one form to another when moving 1 C of charge from A to B the voltage between A and B is 1 V 1 V 1 J 1 C EE201 Lecture 2 P 3 Terminology The voltage drop from A to B is positive The voltage drop from B to A is negative Example V A B If a particle of charge 10 12 C placed at A has a kinetic energy of 10 10 J at B what is the voltage between the two plates EE201 Lecture 2 P 4 Solution Using Eqn 1 9 x V 10 10 J 10 12 C Potential difference or Voltage 100 V Convention 2 methods to denote voltage drop 1 VAB If positive the potential at point A is higher than the potential at B VAB VBA e g V12 Vxy Vca 2 labels Voltage drop from point marked to point marked e g B Vo A If Vo is positive potential B potential A If Vo is negative potential A potential B EE201 Lecture 2 P 5 Example Vy A B Vx 3V VZ D 2 V C Given VBA 4 V what are Vx Vy Vz VBC VCD VAD EE201 Lecture 2 P 6 Solution Vy A B Vx 3V VZ D 2 V C Vx 4 V Vy 4 V Vz 1 V VBC 3 V VCD 2 V VAD 1 V EE201 Lecture 2 P 7 As in the case of current there are dc ac and general voltage waveforms Power A Io 0 Io 0 C E 1 B C E 2 If VAB is positive and constant and Io is constant and no voltage drop in connectors then as current flows through CE 2 energy is converted in CE 2 CE 2 absorbs energy EE201 Lecture 2 P 8 The labeling of voltage and current above is consistent with the passive sign convention C E 2 is a passive circuit element only absorbs energy In CE 2 Energy converted voltage drop x charge Energy converted VAB x Io x t Power energy converted time Power VAB x Io x t t VABIo EE201 Lecture 2 P 9 In going from B to A through CE 1 work must be done against the electric field to move the charge from a lower to a higher potential CE 1 generates electrical potential energy Principle of Conservation of Power The sum of powers absorbed by all elements in a circuit is zero at any instant in time Equivalently the sum of the absorbed power equals the sum of the generated power at each instant in time Unit of power is Watt W EE201 Lecture 2 P 10 Power and Energy Relationships DC Voltage and Current P VoIo 1 10 W P x t 1 11 Time dependent Voltage and Current Instantaneous power p t v t i t 1 12 Energy absorbed in time interval to t W to t t to p d 1 13 EE201 Lecture 2 P 11 Ideal battery or dc voltage source I Vo Circuit Vo Voltage drop is Vo 0 from long dash side to short dash side An ideal battery can deliver constant voltage regardless of current drawn by the circuit V EE201 Lecture 2 P 12 Ideal voltage source v t Circuit v t Circuit Supplies voltage v t regardless of circuit currents Ideal current source i t Circuit i t Circuit Supplies current i t regardless of circuit voltages EE201 Lecture 2 P 13 Ideal dc voltage and current sources I V Circuit Vo V Voltage is Vo with high potential at terminal An voltage source can deliver constant voltage regardless of current through the circuit I I Circuit Io V Current is Io with positive direction along arrow An ideal current source can deliver constant current regardless of voltage drop across the circuit EE201 Lecture 2 P 14 Common voltage and current source labeling i t v t i t v t Consider C E 1 Note Power is generated by source if p t v t i t 0 Power is absorbed by source if p t v t i t 0 This differs from passive sign convention
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