ELECTRIC CIRCUITS 



129 



and the current in the lead between the first and second branches 

 is zero. 



(3) If an alternating e.m.f. E of the wave shape shown in Fig. 

 99 (a) is impressed on the terminals of the circuit AB find the 

 currents in the various branches. 



The e.m.f. wave consists of a fundamental sine wave of effective 

 value 100 volts at 50 cycles and a fifth harmonic of effective 

 value 10 volts. 



Impressed E.M.F. 



Fundamental 



(1) 



(2) 



(3) 



Fifth Harmonic 



(6) 



- =4.8 



(d) 



Fundamental Currents 

 and E.M.F. 



Fifth Harmonic 

 Current andE.M.F. 



FIG. 99. 



The resistance of branch (1) is 10 ohms; the reactance of 

 branch (2) is 10 ohms at 50 cycles and 50 ohms at 250 cycles; 

 the condensive reactance of branch (3) is 10 ohms at 50 cycles 

 and 2 ohms at 250 cycles. 



The current /i in (1) consists of a fundamental of J T rr- = 10 

 amperes and a fifth harmonic of | = 1 ampere in phase with 

 their respective e.m.f. 's. 



The wave shape of the current in the resistance is the same as 

 that of the impressed e.m.f. 



The current /2 in (2) consists of a fundamental of ^Q- = 10 

 amperes and a fifth harmonic of $ = 0.2 ampere in quadrature 

 behind 'the e.m.f .'s producing them. The fifth harmonic is not 

 nearly so prominent as in the resistance circuit and thus react- 

 ance tends to smooth out irregular waves and make them more 

 nearly approximate to sine waves. 



The current /a in (3) consists of a fundamental of J T o a = 10 



