298 



BELL SYSTEM TECHNICAL JOURNAL 



quad, the surrounding wires and the lead sheath are not included in these 

 computations. 



These values assume a temperature of 20° Centigrade (68° Fahrenheit) 

 but if the temperature varies, so also does the resistance. Figure 3 shows 

 the a-c. temperature coefficient of resistance and its variation with tem- 

 perature for 19-gauge pairs in ohms per ohm per degree, Fahrenheit, i.e., 



FREQUENCY-CYCLES 



VDC. RESISTANCE-OHMS PER 1000 LINEAR FEET 



Fig. 2 — Skin effect and proximity effect on a.-c. resistance of toll cable pairs 



A = - — 

 Ri dt 



(3) 



where A is the a-c. temperature coefficient of resistance of copper at h 

 degrees, Fahrenheit. The a-c. resistance R at temperature / is given by 

 the formula 



R= RA^^ A{t - h)] 



(4) 



where Ri is the a-c. resistance at temperature h degrees, Fahrenheit. The 

 coefficient A decreases with increasing frequency, but not indefinitely; it 

 approaches 1/2 the d-c. coefficient as its asymptotic limit with frequency. 



