. A text-book of electrical engineering;. .e. from — to + , the 79- Effect of Phase Difference on Power 257 apparatus is acting momentarily as a generator and returning electricalenergy to the circuit. Fig. 254 refers to a coil or other apparatus in which the current / lags byan angle 0 behind the terminal pressure. This lag is due to the self-induc-tion of the coil. The time is plotted as abscissae and the current and asordinates. The angle 0 by which the current lags behind the correspondsto the time AB. A curve is now plotted giving the momentary values of the power foundby m
. A text-book of electrical engineering;. .e. from — to + , the 79- Effect of Phase Difference on Power 257 apparatus is acting momentarily as a generator and returning electricalenergy to the circuit. Fig. 254 refers to a coil or other apparatus in which the current / lags byan angle 0 behind the terminal pressure. This lag is due to the self-induc-tion of the coil. The time is plotted as abscissae and the current and asordinates. The angle 0 by which the current lags behind the correspondsto the time AB. A curve is now plotted giving the momentary values of the power foundby multiplying together the corresponding values of current and Thesevalues of the power are positive during the intervals OA and BC, but nega-tive during the shorter intervals AB and CD, as shown by the dotted curveP, which represents the rapidly changing power to a certain scale. The areaenclosed between this curve and the horizontal axis represents the energysupplied to the apparatus. This area lies partly above the axis and partly. Fig- 254 below. The mean power is found by subtracting the area below the linefrom the area above the line, and dividing the difference by the time. It isevident that the power supplied to the apparatus is less than we shouldexpect from multiplying together the pressure and the current as read onsuitable instruments. In order to calculate the mean power, we shall imagine the curves to beplotted to a base representing the angular movement of the vector, instead A of the time. If the strength of the current at a given moment be i. sin a, the A terminal pressure at the same moment will be v. sin (a + ^), and the momen-tary value of the power will be equal to their product, thus A A P = !;.». {a + <p). We may imagine this power to remain constant over the infinitely smallangle da, so that the area of an infinitely narrow vertical strip will be = (a + <f}),da. T. E. 17 258 Electrical Engineeririg The mean value of t
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