RESISTANCE AND ELECTROMOTIVE FORCE. 53 



23. A pure copper wire, 2,000 feet long weighs 125 pounds. 

 What is its resistance at 20 C. How will its resistance be 

 changed by doubling the length without changing its weight ? 

 The specific gravity of copper is 8.9. Ans. i.oi ohms. 



24. The specific resistance of carbon such as used for arc lamps 

 is about 2,400. times as great as that of pure copper. Find the 

 watts lost, that is, find Ri 2 , in the two carbons of an arc lamp, 8 

 inches of each carbon being in circuit, the carbon being J inch in 

 diameter, and the current passing through the lamp being 9.6 

 amperes. Ans. 12.3 watts. 



25. A column of a 1 5 per cent solution of CuSO 4 , I meter 

 long, having one square millimeter section, has a resistance of 

 260,000 ohms. An electrolytic cell of this solution has two flat 

 electrodes, 30 x 30 centimeters, 2.5 centimeters apart. Calculate 

 the current due to 2 volts between electrodes, allowing 0.2 volt 

 for polarization. Ans. 27.7 amperes. 



26. A copper transmission line has a resistance of 5 ohms at 

 20 C. What is its resistance at 90 C. ? Ans. 6.297 ohms. 



Note. The difference between the temperature coefficient of resistance of a metal 

 expressed as a fraction of its resistance at o C. and its temperature coefficient 

 expressed as a fraction of its resistance at any other temperature not greatly different 

 from o C. is less than the variations of the temperature coefficient for different 

 samples of the same (commercial) metal, and therefore it is ridiculous to insist on 

 the refined calculations which grow out of the above-mentioned difference. The 

 answers to all temperature-resistance problems in this collection are, however, found 

 by the correct (arithmetically correct !) method. The formula is 



R 



27. A wire has a resistance of 164.8 ohms at 20 C. and a 

 resistance of 186.2 ohms at 70 C. What is the mean tempera- 

 ture coefficient? Ans. 0.002739. 



28. The field coil of a dynamo has a resistance of 42.6 ohms 

 after the dynamo has stood for a long time in a room at 20 C. 

 After several hours' running the resistance of the coil is 51.6 

 ohms. What is its temperature? Ans. 76.5. 



29. A platinum wire has 254 ohms resistance at o C. When 



