CHAPTER XI 

 SYMBOLIC EXPRESSIONS AND METHODS 



1. A current of 10 amperes lags 30 degrees behind the impressed 

 e.m.f. of 100 volts. Find graphically the conductance, suscept- 

 ance and admittance regarding these as constants which multiplied 

 by the e.m.f. give the power and wattless components of the current 

 and the current itself. Check by finding the relation of these 

 quantities to the resistance, reactance and impedance. (4 min.) 



2. Required symbolic expressions for the following vectors at 

 the angles given: (a) 3.2 cm., 25 degrees; (b) 6.0 cm., 100 degrees; 

 (c) 4.1 cm., 225 degrees; (d) the vector sum of (a) and (c). Check 

 graphically. (15 min.} 



3. Give symbolic expressions for the following vectors arid for 

 their sum: 1", tan- 1 }; 2", tan- 1 2; 3", tan- ! (- 1). (5 min.} 



4. Obtain symbolic expressions for e.m.f.'s of 20 volts, making 

 -f 30 degrees with horizontal; and 30 volts making + 45 degrees; 

 give the expression for their sum and find its absolute value and 

 the tangent of its angle; also check graphically. (10 min.) 



5. The e.m.f.'s around two reactive circuits in series are 20 and 

 30 volts, and the power factors are 0.5 and 0.707. Find by 

 symbolic method the combined e.m.f. (3 min.) 



6. Two currents of 10 and 15 amperes in parallel circuits lag 

 behind the e.m.f. by angles tan~*| and tan -1 ; by symbolic method 

 find sum and its angle of lag. (5 min.) 



7. Two series circuits having resistances of 3 and 4 ohms and 

 inductances of 0.01 and 0.05 henry are in series upon a 100-period 

 system, and take 5 amperes; obtain the symbolic expression for 

 the e.m.f. and also its absolute value and lag. (5 min.} 



8. Solve problem 5, Chapter V, by the symbolic method. 

 (6 min.) 



9. Solve problem 6, Chapter V, by the symbolic method. 

 (20 min.} 



10. Two parallel circuits have resistances of 8 and 3 and re- 

 actances of 6 and 4; find the conductance, susceptance and the 

 admittance of the combined circuits; also with 100 volts applied 



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