510 ALTERNATING CURRENTS 



PROBLEMS ON CHAPTER XIII 



167. A sphere has a radius of 2 ft. (a) How many steradians or unit 

 solid angles will an area of 4 sq. ft. on its surface subtend? (6) 5 sq. ft.? 



168. Repeat problem 157 for a sphere whose radius is 3 ft. 



159. A light source has a mean spherical intensity of 40 candles. How 

 many lumens does it emit? 



160. A light source has a mean spherical intensity of 40 candles, (a) 

 How many lumens will fall on the inside surface of a sphere of 2 ft. radius 

 having the light source at its center, assuming that the light radiates with 

 equal intensity in all directions. (6) How many lumens will fall on an 

 are of 4 sq. ft. on this surface? 



161. Determine the illumination in foot-candles in (a) and (6), problem 

 160. 



162. A certain lamp is equipped with a reflector which sends all the 

 light into the lower hemisphere. This light has a mean lower hemispherical 

 candlepower of 200. How much light flux (in lumens) does this lamp emit? 



163. The candlepower of the lamp in problem 162 at a 45 angle is 250. 

 What is the illumination in foot-candles on a surface 10 ft. from this lamp 

 when the surface is perpendicular to the direction of the light? 



164. A certain lamp placed 25 ft. above the street has an intensity of 400 

 candlepower in a vertically downward direction. What is the illumination 

 on the street directly below the lamp? 



165. W T hat does the illumination in problem 164 become if the lamp is 

 raised 5 ft. ? 



166. A nitrogen-filled lamp has a rating of 110 m.s.cp. If it takes 0.9 

 amp. at 110 volts, what is its efficiency in watts per mean spherical candle- 

 power? In lumens per watt? 



167. A tungsten vacuum lamp takes 0.52 amp. at 115 volts and is rated 

 at 50 m.h.cp. What is the efficiency in watts per mean horizontal candle- 

 power? In lumens per watt if the spherical reduction factor is 0.75? 



168. One-hundred watt tungsten vacuum lamps are furnished by a 

 lighting company at 20 cts. each. Seventy-five watt gas-filled lamps are 

 supplied at 50 cts. each. Assuming that the candlepower of each is prac- 

 tically the same and that energy costs 8 cts. per kw.-hr., how many hours 

 must the lamps burn before the total cost of the two is the same? 



169. Assuming that each lamp of problem 168 has a life of 1,000 hr., 

 at what cost of energy per kilowatt hour will the total cost of the lamps be 

 equal? 



170. In a series direct-current open-arc lamp the arc itself takes 450 watts 

 and the current is 9.6 amp. The mean spherical candlepower is 410 and 

 the maximum candlepower in an obliquely downwards direction (see Fig. 

 383, page 426) is 1,200 cp. (a) What is the efficiency in watts per mean 

 spherical candlepower? (b) In lumens per watt? 



171. Repeat problem 170, giving (a) and (b) when the arc lamp is supplied 

 from 115-volt multiple mains. 



