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Unformatted text preview: inductance, V L = jwLlL, and the voltage leads the current by 90°. For a capacitance, V c = -j(1/wC)Ic, and the voltage lags the current by 90°. 7. Many techniques learned in Chapter 2 for resistive circuits can be applied directly to sinusoidal circuits if the currents and volt- ages are replaced by phasors and the pas- sive circuit elements are replaced by their complex impedances. For example, complex impedances can be combined in series or parallel in the same way as resistances (except that complex arithmetic must be used). Node voltages, the current-division principle, and the voltage-division principle also apply to ac cir- cuits. 8. When a sinusoidal current flows through a sinu- soidal voltage, the average power delivered is P = Vrmslrms cos( e), where e is the power angle, which is found by subtracting the phase angle of the current from the phase angle of the voltage (i.e., e = ev - ei). The power factor is cos(e). 9. Reactive power is the flow of energy back and forth between the source and energy-storage ele- ments (L and C). We define reactive power to be positive for an inductance and negative for a capacitance. The net energy transferred per cycle by reactive power flow is zero. Reactive power is important because a power distribu- tion system must have higher current ratings if Problems Section 5.1: Sinusoidal Currents and Voltages P5.1. What are the units for angular frequency w? For frequency f? What is the relationship between them? P5.2. Consider the plot of the sinusoidal voltage v(t) = V m cos(wt +e) shown in Figure 5.1 on page 216. Which of the numbered statements below best describes: a. decreasing the peak amplitude V m? b. increasing the frequency f? c. increasing e? d. decreasing the angular frequency w? e. increasing the period? Problems 273 reactive power flows than would be required for zero reactive power. 10. Apparent power is the product of rms voltage and rms current. Many useful relationships between power, reactive power, apparent power, and the power angle can be obtained from the power triangle shown in Figure 5.23 on page 243. 11. In steady state, a network composed of resis- tances, inductances, capacitances, and sinu- soidal sources (all of the same frequency) has a Thevenin equivalent consisting of a phasor volt- age source in series with a complex impedance. The Norton equivalent consists of a phasor current source in parallel with the Thevenin impedance. 12. For maximum-power transfer from a two- terminal ac circuit to a load, the load impedance is selected to be the complex conjugate of the Thevenin impedance. If the load is constrained to be a pure resistance, the value for maximum power transfer is equal to the magnitude of the Thevenin impedance....
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This document was uploaded on 02/14/2012.
- Spring '09