268 ADVANCED ELECTRICITY AND MAGNETISM. 



direction from the center of the initial distribution will be entirely 

 devoid of voltage and current; a two mile section beyond the 

 4-mile blank section and to the right will have over it a uniform 

 voltage of + 2,500 volts and a uniform current of + 25 amperes; 

 and a two mile section beyond the 4-mile blank section and to the 

 left will have over it a uniform voltage of + 7,500 volts and a 

 uniform current of 75 amperes. 



26. Calculate the leakage resistance (insulation resistance) 

 of one mile of the line in problem 4 in order that the line might 

 give distortionless transmission. Ans. 670,000 ohms. 



Note. The leakage resistance here required is very much less than the leakage 

 resistance of a well-constructed line in good condition in dry weather. In wet 

 weather, however, the leakage resistance falls off and may give rise to approximately 

 distortionless transmission. This is the cause of the remarkable clearness of tele- 

 phonic transmission which is sometimes obtained over a moderately long line in 

 wet weather. 



27. A current of 10 amperes is left to die away in a circuit of 

 which the resistance is 2 ohms and the inductance is o.oi henry. 

 What is the value of the current after 0.06 second? Ans. 

 0.0000605 ampere. 



Note. See Art. 37. 



28. A io-microfarad condenser is charged by a loo-volt battery 

 and allowed to stand and lose its charge by leakage. The insula- 

 tion resistance of the condenser is 1 ,000,000 ohms. What is the 

 voltage across the condenser after 23.25 seconds. Ans. 10 volts. 



Note. Let q be the decreasing charge on the condenser / seconds after it is 

 left standing and let e be the corresponding electromotive force across the con- 

 da de dq 

 denser terminals. Then q=Ce and = C ; but is the leakage current 



at at at 



and it is equal to , where R is the insulation resistance of the condenser. 

 R 



Therefore - C - or 75 so that log e = --+ a constant. 

 K at e CK uA. 



29. A 2O-mile metallic circuit telephone line consists of two 

 No. 14 B. & S. copper wires 18 inches apart center to center. 

 Find the resistance of the line per mile. Find inductance and 

 capacity of the line per mile. Find leakage resistance between 



