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A sine wave is the signature of AC It has two alternations per hertz, or cycle It is the alternation that is examined This is to obtain the rms, the peak value Em and the average values Eav of AC See Figure 14-5
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The abbreviation rms means root-mean-square, the value used when a meter is calibrated to read voltage or current When we say 120volts AC, we really mean it is 120-volts rms The rms is a way of equating AC and DC It is the heating effect of AC compared to DC
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FIGURE 14-5 A sine wave is the signature of alternating current
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A DC power source provides a steady voltage that rises almost instantaneously and stays at that level with no cooling period AC varies, causing the resistor to heat up slowly and then cool down This is why AC has only 7071% of the heating value of an equal amount of DC Remember this when comparing AC and DC systems
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PEAK VALUE
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Peak is the maximum or highest point on the sine wave To convert rms to peak, multiply by 1414 A 120-volt rms thus has a 16968-volt peak Peak-to-peak (p-p) is a term used to describe the signal voltage in television receivers It is a term used more with electronics than with electrical work
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CHAPTER FOURTEEN
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TABLE 14-3 Formulas for Motor Applications
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T = torque or twisting moment (force moment arm length) p = 31416 N = revolutions per minute HP = horsepower (33,000 lb-ft per min) applies to power output R = radius of pulley, in feet E = input voltage I = current in amperes P = power input in watts 63, 025 HP = T(oz-in) N 9917 10 7 = approx T (oz-in) N 10 6 HP 746 P = EI power factor = motor efficiency Power to Drive Pumps HP = gal per min total head (including friction) 3960 eff of pump HP = T (lb in) N (rpm)
where pipe length (ft) [velocity of flow (fps)]2 002 Approx friction head (ft)= 5367 diameter (in) Eff = Approx 050 to 085 Time to Change Speed of Rotating Mass Time (sec) = where WR 2 (disc) = WR (rim) =
WR 2 change in rpm 308 torque (lb- ft) Weight(lb) [radius (ft)2 ] 2 Wt (lb) [(outer radius in ft)2 + (inner radius in ft)2 ] 2 Power to Drive Fans
HP =
Cu ft air per min water gage pressure (in) 6350 eff
ELECTRICAL AND ELECTRONIC FORMULAS
AVERAGE VALUE
The average value of a sine wave function is de ned as the area under one loop divided by the base of the loop It is the average value of AC being delivered The base of one loop is 180 or pi (p) radians in length However, in order to nd the area of such an irregular surface as a sine loop, the gure must be broken down into a series of small rectangles, the areas of which can be easily determined The sum of all these small areas will then be the area of the loop To convert from peak to average, multiply by 0637 The 16968volt peak (given earlier) would then have an average of 108
FORMULAS USED WITH MOTORS
Working with motors sometimes requires the use of special formulas for example, to gure the horsepower of a motor or to determine the power needed to drive a pump or a fan Table 143 gives abbreviations used in dealing with motors and useful formulas
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Basic Electronics
Electronics got its start with the invention of the vacuum tube A vacuum tube has the ability to rectify and to amplify Edison was experimenting with his rst electric lamp when he discovered that the frequent burning out of the carbon lament near the positive end produced a black deposit inside the bulb and a shadow on the positive leg of the lamp lament He tried to remedy the condition by placing a metal plate inside the lamp near the lament and connecting it through a galvanometer to the lament battery When the positive terminal was connected to the metal plate, a de ection of the galvanometer was observed When the plate was connected to the negative terminal, there was no de ection of the galvanometer Edison recorded these effects in his notebook but did not pursue the phenomenon Sir J J Thomson, an English physicist, discovered the electron around the turn of the century Once the electron was discovered and de ned, it was an easy task to describe what happened during the Edison effect Electrons escaped from the heated carbon lament and, being negatively charged, moved freely through the vacuum to the plate when it was connected to the positive battery terminal However, when the plate was negative, the electrons were repelled, and no de ection was observed on the galvanometer The vacuum tube diode was the rst device to take advantage of the Edison effect It was made to rectify alternating current (AC) that is, to change the AC to direct current (DC)
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