Question 2.1: RMS value of a Square Wave. Find the rms value of a squarewa......

RMS value of a Square Wave. Find the rms value of a squarewave current that jumps back and forth from 0 to 2 A as shown below:

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We need to find the square root of the average value of the square of the current. The waveform for current squared is (Figure 1)

The average value of current squared is 2 by inspection (half the time it is zero, half the time it is 4):

$I_{rms} = \sqrt{\left(i^{2}\right)_{avg}} = \sqrt{2} A$

Question: 2.13

Neutral-Line Current. A four-wire, wye-connected balanced load has phase currents described by the following harmonics: ...

Only the harmonics divisible by three will contrib...
Question: 2.2

Wall outlet voltage. Find an equation like (2.1) for the 120-V, 60-Hz voltage delivered to your home. ...

From (2.11), the amplitude (magnitude, peak value)...
Question: 2.12

Harmonic Distortion for a CFL. A harmonic analysis of the current drawn by a CFL yields the following data. Find the rms value of current and the total harmonic distortion (THD). ...

From (2.94) the rms value of current is I_{...
Question: 2.11

Harmonic Analysis of a Square Wave. Find the Fourier series equivalent of the square wave in Fig. 2.31a, assuming that it has a peak value of 1 V. ...

We know by inspection, using (2.83) to (2.86), tha...
Question: 2.10

Correcting the Power Factor in a Three-Phase Circuit. Suppose that a shop is served with a three-phase, 208-V transformer. The real power demand of 80 kW is mostly single-phase motors, which cause the power factor to be a rather poor 0.5. Find the total apparent power, the individual line currents, ...

Before correction, with 80 kW of real power being ...
Question: 2.9

Currents in a Single-Phase, Three-Wire System. A three-wire, 120/240-V system supplies a residential load of 1200 W at 120 V on phase A, 2400 W at 120 V on phase B, and 4800 W at 240 V. The power factor for each load is 1.0. Find the currents in each of the three legs. ...

The 1200-W load at 120 V draws 10 A; the 2400-W lo...
Question: 2.8

Power-Factor-Correcting Capacitor for a Motor What size capacitor would be needed to correct the power factor of the 230-V, 60-Hz, 5-hp motor in Example 2.6? ...

The capacitor must provide 4.40 kVAR of capacitive...
Question: 2.7

Avoiding a New Transformer by Improving the Power Factor. A factory with a nearly fully loaded transformer delivers 600 kVA at a power factor of 0.75. Anticipated growth in power demand in the near future is 20%. How many kVAR of capacitance should be added to accommodate this growth so they don’t ...

At PF = 0.75, the real power delivered at present ...
Question: 2.6

Power Triangle for a Motor. A 230-V induction motor draws 25 A of current while delivering 3700 W of power to its shaft. Draw its power triangle. ...

\begin{matrix}\quad \quad \text{Real power}...