124 ELECTRICAL ENGINEERING 



82. Numerical Examples. (1) If an alternating e.m.f. of 200 

 volts at a frequency of 60 cycles per second is impressed on a 

 circuit consisting of a resistance of 10 ohms in series with an in- 

 ductance of 0.1 henry and a capacity of 100 microfarads, (a) deter- 

 mine the current in the circuit and its phase relation with the 

 impressed e.m.f., (b) the e.m.f. consumed in each part of the cir- 

 cuit, (c) If the impressed e.m.f is maintained constant and the 

 frequency is varied determine the maximum value of the current. 



(a) The inductive reactance of the circuit is 



X = 27T/L = 2 X 3.14 X 60 X 0.1 = 37.6 ohms; 

 the condensive reactance is 



= 26.4 ohms; 



27T/C 2X3.14X60X100 

 the impedance of the circuit is 



Z = VR* + (X - X c ) 2 = VlO 2 + (37.6 - 26.4) 2 = 15 ohms; 



and therefore the current is 



E 200 

 I = ~ = -YR- = 13.3 amperes. 



/- I i 



The current lags behind the e.m.f. by an angle 0, where 

 X - X e 37.6 - 26.4 



tan * = TT -16- 



and <t> = 4818 / . 



(b) The e.m.f. consumed in the resistance is 



E l = IR = 13.3 X 10 = 133 volts; 



the e.m.f. consumed in the inductive reactance is 



E 2 = IX = 13.3 X 37.6 = 500 volts; 



and the e.m.f. consumed by the condensive reactance is 

 E s = IX C = 20 X 26.4 = 350 volts. 



The impressed e.m.f. is 



E = VES + (E 2 - # 3 ) 2 = Vl33 2 + (500 - 350) 2 = 200 volts. 

 The vector diagram is shown in Fig. 95. 



