USE OF ELECTRODYNAMOMETER WITH ALTERNATING CURRENTS. 29 1 



ordinary electrodynamometer, in which the axes of the two coils 

 are rectangular, the difference of phase is given by the expression 



tan 27^ = 



in which L and L', r and r' are the coefficients of self-induction and 

 the resistances of the two coils. 



The difference of phase is zero if we have 



that is to say, if the resistances are proportional to their coefficients 

 of self-induction. This condition is realised for two similar coils. 



In the general case, as the difference of phase is between 



and - , sin 2 ir\j/ is between and - ; consequently for given 

 4 2 



intensities of the two currents, the factor in the brackets in equa- 

 tion (56) may vary from to - , according to the difference of 



2 



phase, which depends on the resistance and the coefficients of in- 

 duction of the two coils. 



When the resistance r' and the coefficient of self-induction L' 

 of the movable coil are very great in comparison with those of 

 the fixed coil, we have sensibly 



L- r L 



27T r' L' 27rL' r' L' 



tan 27ru/ = - 



T r 47T 2 L 



904. Suppose, finally, that in order to measure a sinusoidal 

 current we join in series the two coils of an electrodynamometer, 

 of which r' and L' are the total resistance and the coefficient of 

 self-induction, and that we shunt the instrument at two points of 

 the principal circuit, between which is a wire whose elements are 

 r and L, and let M be the coefficient of mutual induction of the 



U 2 



