ALTERNATING CURRENTS. 52! 



If the frame turns in a uniform magnetic field, with a constant 

 angular velocity o> = , the electromotive force of induction for a 

 deflection x, provided we choose conveniently the origin of the 

 time /, may be written 



HS cos x- wHS cos x = wHS sin 2?r . 

 at I 



When the permanent regime is established (535), the current 

 is of the form 



I = A sin 27r ( - 

 and we have 



o> 2 H 2 S 2 



T 2 



The mean square I" 2 of the intensity is 



which gives 

 (7) 



The measurement of the mean square of the intensity I" 2 by an 

 electrodynamometer, or by a calorimetrical method, will give the 

 resistance R of the circuit. Two observations, made with different 

 velocities, will enable us to eliminate the coefficient L of self-induction. 



Instead of rotating the frame, we may rotate, at a uniform speed, 

 a magnet placed in the centre. For an angle x of the magnet with 

 the plane of the frame, the value of the electromotive force of 

 induction is 



GM cos x = wGM cos x . 

 at 



It is sufficient if, in expression (7), we replace the product HS 

 by GM; consequently 



(8); R* 



