ELECTRICAL WAVES AND SOME OF ITS APPLICATION’S. 
21 
Fig. 5. 
Let M be the coefficient of mutual inductance between the two branches. 
Let X and y be currents in branches ACB, ADB respectively. 
It is shown (‘ Becent Besearches,’ p. 513) that for a rapidly-alternating’ current of 
frequency n, where = 2Trn, that 
X — 
V = 
S^ + (N - M)Bd 
(L + N - 2M)2 + (R -I S)2 
_ W + (L - M)2p3 1 
[(L -f N-2Mf+ (E -f S)L 
cos [pt 4- e) = A cos {pt “b e), say 
cos (p/i -f- e') = B cos {'pt -b e'), 
^ p{E(N-M)-S(L-M)} 
S(R + S) -h (L + N - 2M) (N - ’ 
tan e 
p{R(N-M)- S(L-M)} 
R (R + S) -f (L -h N - 2M) (L - U) ’ 
A and B are the maximum currents in the two branches ACB, ADB respectively, 
and 
A_ /s^anHEZZ. 
B V py + (L _ M)2’ 
If the circuits be so adjusted that A = B 
B^ + (L - + (N - M)2 p\ 
and 
3_ Pd - 
N2 -L~- 211 (N - L) ’ 
The value of the impedance \/B^+^AL‘^ is nearly independent of B for rapid 
frequencies in ordinary copper wire circuits 
Suppose 
n = 10®, p = 277. 10®, and L = 10^ 
then 
jdL2 = 47rM02o. 
If the value of B for the particular period was 2 ohms say, then 
Jd_ 
a very small quantity. 
