THE MEASUREMENT OF CURRENT 65 



If R a = R a f , then by symmetry i a = v and ib = i 2i a . 

 Making this substitution and arranging terms 



(R a + 2R b )i a + (3L + Ma* - *M*) = R b i + (L - M*)j t 

 Assuming sinusoidal currents 



(Ra + 2R b )I a + JO>(3L + M aa . - 4Mab)Ia 



= Rj'+jafr - Mob) I (36) 



.'. \(R a + 2/W 2 + " 2 (3L + M an , - 



Solving for 



) 2 )/ 2 (37) 



At low frequencies, denoted by the subscript 0, where the 

 inductance effects are negligible, 



i/ )o - = 2 + ^ = 2.986 (36a) 



\J-a)o fi b 



and 



7FV - 1 + 2^ b = 3.029 (37a) 



At frequencies so high that the resistance effects are swamped 

 by those of inductance, these ratios become 



_ _., 



/a " L-M* 



I _8L + M^-43f^ 



/. L + M o - - = 3 ' 312 



and 



f: 



From the data given, at any frequency, /, by (36) and (37) 



//a 2 /0. 12 

 \ / 2 = \ 1.10 



124 + 0.363 X IP" 12 / 2 

 105 + 2.98 X 10- I2 f* 



/0. 120 + 0.272 X 10- 12 / 2 

 \1.105 + 2.98 X 10~ 12 / 2 



