Intermediate physics / by W. Watson.

  • Watson, W. (William), 1868-1919.
Date:
1912
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Licence: In copyright

Credit: Intermediate physics / by W. Watson. Source: Wellcome Collection.

Provider: This material has been provided by UCL Library Services. The original may be consulted at UCL (University College London)

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    mum value of the E.M.F. If the coil is connected to an external circuit and the resistance of the whole circuit is fairly high compared with the self-induction, an alternating current will be produced in the circuit, such that c=C sin ot . . . . (182) where c is the instantaneous value of the current at the time t and C is the maximum value. Since, if T is the time the coil takes to complete one revolution, o = 27r/T, we have c=asin^ . . . . (183) Although in the case of an alternating-current dynamo the relation between the E.M.F. and the time is in general not a swvple sine curve X Fig. 292. (§ 84), yet it so nearly resembles a sine curve that we may for most purposes assume that it is exactly a simple sine curve, and we now pro- ceed to consider some of the properties of alternating currents on this assumption. If we take a sine curve abcde (Fig. 292), such that the length AE is equal to the period T of the alternating current, and the amplitude MB is equal to C, then the ordinates of this curve will give the values of the current c at any time throughout a complete period. An examination of the curve shows that the mean value of c is zero, for the positive loop abc of the curve is equal to the negative loop cde. Since the square of a negative quantity is positive, the value of is always positive, the values of being shown by the dotted curve afcge. Now since sin^ 0 = ^(1 - cos 29), we have = U sm^ — = -—■ cos —- T 2 2 T 4:77t Now it can easily be shown that the mean value of cos —^ throughout a period is zero, for by plotting the value of this quantity we should obtain a curve similar in form to abode on Fig. 292. Hence the 7nean