INDUCTANCE AND CAPACITY 367 



as e makes contact with 6, the varying current i c flows into 

 the condenser, causing temporary alterations in the currents 

 through M, N } R G , B, and P. The change in P.D. between the 

 terminals of any one of the resistances is the change in the cur- 

 rent multiplied by the resistance. The currents d! B , 8I G , etc., 

 are variable and become zero when the condenser is fully charged. 

 Referring to Fig. 215 it will be seen that 



81 M = ic + 8I G 

 81 B = dI M + 51 N 

 dip = 81 B ic 

 8I P = 8I G + 81 N 



81 AT == 81 B 1>C 8I G . 



Using the changes in the currents, Kirchhoff's laws may be applied 

 to the meshes M R G N and B N P and by using the above 

 relations the resulting equations may be expressed in terms of 

 the resistances and the variable currents 8I B , 8I G and i c . 

 For the mesh M R G N at any instant during charging, 



+ R a (Sl ) + - N(&I X ) = 



or 



M(i c + dla) + R G (8I G ) + Ld( ^ 6) ~ N W* ~ *c - 57 ) = 0- 



Uniting terms gives 

 i c (M + N) + 8I G (M + R G + N)- N(8I B ) + L ^ /Q) = 0. (3) 



For the mesh B N P at any instant during charging, 

 B(dI B ) + N(8I B - i c - 8I G ) + P(8I B - i c ) = 

 or uniting terms 



- i c ( N + P) - 8I G (N) + &I B (N + P + B) = 0. (4) 



Equations (3) and (4) may be integrated to obtain the total 

 quantities displaced by the variable currents during the charging 

 of the condenser; 8I G is zero at both limits. Therefore 



Q C (M + N) + Q (M + R G + N) - Q B (N) = (3a) 

 and 



- Qc(N + P) - Q (N) + Q B (N + P + B) = 0. (4o) 



