SINGLE-PHASE POWER, WATTMETERS 71 



the power curves, and find from them the power consumption. 

 What are the power and wattless components of the cur- 

 rent? Take one large division of tin- paper equal to 30 degrees. 

 (20 min.) 



8. Plot the curves and prove graphically, that is by measure- 

 ment of area, that for the following case the watts equal IE cos4>; 

 maximum current, 126; maximum -.iii.f., 1 i<>; lag, 36 degrees. 

 Take one large division equal to 30 degrees. Where is the axis 

 of the power curve relative to the axis of the e.m.f. < u 



min.) 



9. A lamp and an induction coil are in series on a 120-volt 

 system. The coil cuts down the voltage on the lamp to 70 at 

 which it takes 0.15 ampere. The resistance of the coil is 50 ohms. 

 Plot curves of instantaneous power values for the lamp, th< 

 and the combined load. (30 min.) 



10. Draw a sine curve for an e.m.f. of 100 volts maximum, and 

 for a current of 50 amperes with a power factor of 70.7%. From 

 these plot the power curve. Repeat for the same current with a 

 power factor of 0.5, and with zero power factor. (40 min.) 



11. The cost of a certain 10,000-kilovolt-ampere power-plant 

 complete is $80.00 per kilovolt-ampere. If the current supplied 

 by this plant lags 30 degrees what will be the available output in 

 kilowatts, and what is the decrease in the value of the plant as 

 compared with the same plant at unity power factor? (/ min.) 



12. 10,000 kilowatts are transmitted 100 miles at 80,000 volts 

 over a line which has a resistance of 64 ohms. The power factor 

 is 70%. If the power costs the power company 0.6 cents per 

 kilowatt-hour and is used 10 hours a day for 300 days in the year, 

 what would be the annual saving on copper loss if the power factor 

 could be increased to unity? (3 min.) 



13. Separating the two coils of a dynamometer ammeter and 

 sending two currents differing in phase through them, the instru- 

 ment reads 50.3. Ammeters in these two circuits read 7.35 and 

 11.47 amperes; what is the phase angle between the currents? 

 (2 min.} 



14. Required the maximum inductance that the shunt coil of 

 a wattmeter can have if its resistance is 1500, in order that the 

 error with a 100-period current shall not exceed i of 1%. the 

 maximum lag in the circuit to be measured being 45 degrees. 

 (2 min.) 



