Slide 1Slide 2Slide 3Slide 4Slide 5Slide 6Slide 7Slide 8Slide 9Slide 10Slide 11Slide 12Slide 13Slide 14EE201 Lecture 2 P. 1Voltage, Sources, PowerVoltageE--- - - - -+++ + + + +Charged metal plates with E fieldConsider 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.+-ABdEE201 Lecture 2 P. 2Potential 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 VVoltage 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 CEE201 Lecture 2 P. 3Terminology: The voltage drop from ‘A’ to ‘B’ is positive. The voltage drop from ‘B’ to ‘A’ is negative. Example+ + +---+? VAB-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. 4SolutionUsing 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 = - VBAe.g. V12, Vxy, Vca2) +/- labels -- Voltage drop from point marked ‘+’ to point marked ‘-’. e.g.BA+-VoIf Vo is positive, potential (B) > potential (A)If Vo is negative, potential (A) > potential (B)EE201 Lecture 2 P. 5ExampleVyVxVZ+++++-----Given VBA = 4 V, what are Vx, Vy, Vz, VBC, VCD, VAD?-2 VABCD3 VEE201 Lecture 2 P. 6SolutionVyVxVZ+++++-----Vx = -4 V; Vy = 4 V; Vz = -1 V;VBC = 3 V; VCD = 2 V; VAD = 1 V-2 VABCD3 VAs in the case of current, there are dc, ac, and general voltage waveforms.PowerEE201 Lecture 2 P. 7BAIo > 0Io > 0C.E. 1C.E. 2If 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 Power = energy converted / timePower = [VAB x Io x t] / t = VABIo 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 tEE201 Lecture 2 P. 9In 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. 10Power and Energy Relationships: DC Voltage and CurrentP = VoIo (1.10) W = P x t (1.11)Time-dependent Voltage and CurrentInstantaneous power: p(t) = v(t) i(t) (1.12)t W(to,t) = p() d toEnergy absorbed in time interval (to, t):(1.13)EE201 Lecture 2 P. 11Ideal battery or dc voltage source:VoCircuitVoIVVoltage 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.EE201 Lecture 2 P. 12Ideal voltage source:-++-CircuitCircuit-v(t)v(t)CircuitCircuiti(t)-i(t)Ideal current source:Supplies voltage v(t) regardless of circuit currentsSupplies current i(t) regardless of circuit voltagesEE201 Lecture 2 P. 13Ideal dc voltage and current sources:VoIVVoltage is Vo with high potential at “+” terminal. An voltage source can deliver constant voltage regardless of current through the circuit. CircuitI-+CircuitVIoIVCurrent 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. 14i(t)+_v(t)Common voltage and current source labeling.i(t)v(t)+-Note: Power is generated by source if,p(t) = v(t) i(t) > 0Power is absorbed by source if,p(t) = v(t) i(t) < 0This differs from passive sign convention.Consider C.E.
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