PROBLEMS AND EXERCISES. 423 



3. The current running through an incandescent filament of 

 carbon in a lamp was found to be exactly I weber. The 

 difference of potential between the two terminals of the lamp 

 while the current was flowing was found to be 30 volts. What 

 was the resistance of the filament ? 



4. Define specific resistance. Taking the specific resistance V 

 of copper as 1642, calculate the resistance of a kilometre of 

 copper wire whose diameter is I millimetre. Ans. 20*9 ohms. 



5. On measuring the resistance of a piece of No. 30 B. W. G. 

 (covered) copper wire, 18*12 yards long, I found it to have a 

 resistance of 3 *O2 ohms. Another coil of the same wire had a resist- 

 ance of 22*65 ohms ; what length of wire was there in the coil ? 



Ans. 135*9 yards. 



6. Calculate the resistance of a copper conductor one square 

 centimetre in area of cross- section, and long enough to reach 

 from Niagara to New York, reckoning this distance as 480 

 kilometres. Ans. 78-8 ohms. 



7. You have given an unlimited number of Telegraph Daniell's 

 cells (Fig. 77), their E. M. F. being 1*1 volt each, and their 

 average internal resistance being 2*2 ohms each. What will be 

 the strength of the current when five such cells, in series, are 

 connected through a wire whose resistance is 44 ohms ? 



Ans. 0*1 weber per second. 



8. Show in the preceding case that with an infinite number 

 of cells in series ', the current could not possibly exceed 0*5 weber 

 per second. 



9. The specific resistance of guttapercha being 3*5 x io 23 , 

 calculate the number of webers of electricity that would leak in 

 one century through a sheet of guttapercha one centimetre 

 thick and one metre square, whose faces were covered with 

 tinfoil and joined respectively to the poles of a battery of 100 

 Daniell's cells. Ans. 9-7 webers. 



10. Six Daniell's cells, for each of which E = I -05 volts, r = 

 0*5 ohm, are joined in series. Three wires, X, Y, and Z, whose 

 resistances are severally 3, 30, and 300 ohms, can be inserted 

 between the poles of the battery. Determine the current (in 

 webers} which flows when each wire is inserted separately ; also 

 determine that which flows when they are all inserted at once 

 in parallel arc. 



k \ SJfff^T^vL' '" ^ 



r ., itftfc^*- UR *Hfi>i -*' 



*+** rsYt-r ^ r- ----- - /r/ 



