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Instantaneous power Average power RMS Examples

Lecture 20. AC Power Analysis. Instantaneous power Average power RMS Examples. Constant Term. Wave of Twice Original Frequency. Instantaneous Power: p ( t ). For AC circuits, the voltage and current are v ( t ) = V M cos(  t + v ) i ( t ) = I M cos(  t + i )

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Instantaneous power Average power RMS Examples

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  1. Lecture 20. AC Power Analysis • Instantaneous power • Average power • RMS • Examples

  2. Constant Term Wave of Twice Original Frequency Instantaneous Power: p(t) For AC circuits, the voltage and current are v(t) = VM cos(t+v) i(t) = IM cos(t+i) The instantaneous power is simply their product p(t) = v(t) i(t) = VM IM cos(t+v) cos(t+i) = ½VM IM [cos(v- i) + cos(2t+v +i)]

  3. Average Power (P) • Calculate average power (integrate power over one cycle and divide by period) • Recall that passive sign convention says: P > 0, power is being absorbed P < 0, power is being supplied

  4. Average Power: Special Cases • Purely resistive circuit: P = ½ VM IM The power dissipated in a resistor is • Purely reactive circuit: P = 0 • Capacitors and inductors are lossless elements and absorb no average power • A purely reactive network operates in a mode in which it stores energy over one part of the period and releases it over another part

  5. Average Power Summary Does the expression for the resistor power look identical to that for DC circuits?

  6. Effective or RMS Values • Root-mean-square value (formula reads like the name: rms) • For a sinusoid: Irms = IM/2 • For example, AC household outlets are around 120 Volts-rms

  7. Why RMS Values? • The effective/rms current allows us to write average power expressions like those used in dc circuits (i.e., P=I²R), and that relation is really the basis for defining the rms value • The average power (P) is

  8. RMS in Everyday Life • When we buy consumer electronics, the faceplate specifications provide the rms voltage and current values • For example, what is the rms current for a 1200 Watt hairdryer (although there is a small fan in a hairdryer, most of the power goes to a resistive heating element)? • What happens when two hairdryers are turned on at the same time in the bathroom? • How can I determine which uses more electricity---a plasma or an LCD HDTV?

  9. Class Examples • Drill Problems P8-10, P8-11, P8-12

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