sinusoidally with time as given by E E max sin q i i max sin q ACvoltage and current E max i max time t Rotating Vector Description q 45 0 90 0 135 0 180 0 270 ID: 1032348
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1. AC Circuits
2. An alternating current such as that produced by a generator has no direction in the sense that direct current has. The magnitudes vary sinusoidally with time as given by:E = Emax sin qi = imax sin qAC-voltage and currentEmaximaxtime, t
3. Rotating Vector Descriptionq4509001350180027003600ERadius = EmaxE = Emax sin q
4. Effective AC CurrentThe average current in a cycle is zero—half + and half -.imaxBut energy is expended, regardless of direction. So the “root-mean-square” value is
5. One effective ampere is that ac current for which the power is the same as for one ampere of dc current.One effective volt is that ac voltage that gives an effective ampere through a resistance of one ohm.Effective current: ieff = 0.707 imaxEffective voltage: Veff = 0.707 Vmax
6. Pure Resistance in AC CircuitsAa.c. SourceRVVmaximaxVoltageCurrentVoltage and current are in phase, and Ohm’s law applies for effective currents and voltages.Ohm’s law: Veff = ieffR
7. The voltage V peaks first, causing rapid rise in i current which then peaks as the emf goes to zero. Voltage leads (peaks before) the current by 900. Voltage and current are out of phaseTime, tIiCurrent Riset0.63IInductorTime, tIiCurrent Decayt0.37IInductor
8. A Pure Inductor in AC CircuitThe voltage peaks 900 before the current peaks. One builds as the other falls and vice versa.ALVa.c.VmaximaxVoltageCurrentThe reactance may be defined as the nonresistive opposition to the flow of ac current
9. The back emf induced by a changing current provides opposition to current, called inductive reactance XL.Inductive Reactance:
10. AC and CapacitanceThe voltage V peaks ¼ of a cycle after the current i reaches its maximum. The voltage lags the current. Current i and V out of phase.Time, tQmaxqRise in ChargeCapacitort0.63 ITime, tIiCurrent DecayCapacitort0.37 I