498 Mr. 0. Heaviside on Resistance 



it follows that the impedance at A of a non-distorfcional circuit 

 as above described, but of finite length, stopping at B, where 

 x = l, with a resistance of amount Lv inserted at B, is also a 

 constant, viz. the same Lv. To corroborate, take RS = KL 

 and Zj = Lv in the full formula (32). The result is Z x = Lv. 

 The interpretation in this case is that all disturbances sent 

 from A are absorbed completely by the resistance at B imme- 

 diately on arrival, so that the finite circuit behaves as if it 

 were infinitely long. The permanent state due to a steady V 

 at A is arrived at in the time l/v. The impedance and the 

 resistance then become identical. 



14. If, in the case of § 12, we further specialize by taking 

 R=0, K = 0, producing a perfectly insulated circuit of no 

 resistance, the impedance is, as before, Lt; ; but no part of it 

 is resistance, or ever can be, in spite of the identity of phase 

 of V and C. However long we may keep on a steady V at 

 A, we keep the impressed force working at the same rate, the 

 energy being entirely employed in increasing the electric and 

 magnetic energies at the front of the wave, which is unat- 

 tenuated, and cannot return. 



But if we cut the circuit at B, at a finite distance Z, and 

 there insert a resistance hv, the effect is that, as soon as the 

 front of the wave reaches B, the inserted resistance imme- 

 diately becomes the resistance of the whole combination ; 

 or the impedance instantly becomes the resistance, without 

 change of value. 



15. As a last example of singularity, substitute a short- 

 circuit for the terminal resistance hv just mentioned. Since 

 there is now no resistance in any part of the system, if we 

 make the state sinusoidal everywhere, by V sinusoidal at A, 

 R/ must vanish, or V and C be in perpendicular phases, due 

 to the infinite series of to-and-fro reflexions. We now have, 

 by (32), 



„, T , tan (ph/v) T] tan (nllv) .... 



Zz=L P l pli/v = U P^dfiT> ■ ■■ ( 45 > 



if n/27r= frequency, and R' has disappeared. 



If, on the other hand, Y be steady at A, the current in- 

 creases without limit, every reflexion increasing it by the 

 amount Y/Lv at A or at B (according to which end the re- 

 flexion takes place at), which increase then extends itself to 

 B or A at speed v. The magnetic energy mounts up infi- 

 nitely. On the other hand, the electric energy does not, 

 fluctuating perpetually between when the circuit is un- 

 charged, and JSZY 2 when fully charged. The impedance of 

 the circuit to the impressed force at A is Lv for the time 2l/v 



