SELF-INDUCTANCE 7 



since sin 2pT = sin 4n- = 0. Dividing the area by T, we find that 

 the mean value of the square of a sine function over a period equals 

 Y a , i.e. equals half the square of tJie amplitude. Hence the r.m.s. 



value is = 0707 times the amplitude. The amplitude factor ( 1) 



v/a 



for a simple sine wave is thus = 0*707. 



By a similar method, we can find the arithmetic mean value and 

 the form factor of a sine wave. To find the arithmetic mean value, 

 we may determine the area of a half-wave, i.e. the value of the 



T 



[" T 



integral I Y sin pt . dt, and divide this by . Now 

 * o 



Binpt.dt = Y-cos 



L p o p 



4 

 Hence the mean value is T Y, or, since pT 2ir, the mean value is 



2 



-Y, and the form factor ( 1) of a sine wave is thus 



7T 



Y 



\/2 7T 



4. Impressed and Induced e.m.f.'s. Self- 

 inductance 



In order to maintain an alternating current in a circuit, it be- 

 comes necessary to introduce into the circuit a source of alternating 

 e.m.f. The e.m.f. provided by such a source is spoken of as the 

 impressed e.m.f., in order to distinguish it from other e.m.f.'s which 

 are generally called into play as soon as the alternating current begins 

 to flow. 



A current flowing in a circuit gives rise to a definite number of 

 lines of magnetic induction, which become linked with the circuit. 

 By the great principle discovered by Faraday in 1831, any change in 

 the magnetic flux linked with a circuit is accompanied by the induc- 

 tion of an e.m.f. around the circuit ; the direction of the induced e.m.f. 

 being always such as to oppose the change which gives rise to it (Lenz's 

 law). 



Now, since an alternating current is changing from instant to 



