ELECTRIC CIRCUITS 



105 



Thus,, in a circuit of reactance and negligible resistance the 

 impressed e.m.f. is 90 degrees ahead of the current, or the cur- 

 rent lags 90 degrees behind the impressed e.m.f. 



75. Resistance and Reactance in Series. If a circuit con- 

 tains a resistance R and a reactance X in series and carries an 

 alternating current i = I sin 2 irft, determine the value of the 

 impressed e.m.f. and its phase relation with the current. (Fig. 76.) 



Curve 



FIG. 76. Resistance and reactance in series. 



To drive a current i = 7 sin 2 irft (curve 1) through a resist- 

 ance R an e.m.f. is required equal to 



CR iR = I Q R sin 2irft (curve 2), 



a sine wave in phase with the current with a maximum value 

 I R. 



The inductance of the circuit sets up a back e.m.f., 



di 



e b =-L 



dt 



2 TT/L/O sin (2 wft - 90) (curve 3), 



a sine wave lagging 90 degrees behind the current with a maxi- 

 mum value 2 TT/L/O = IoX. 



To overcome this back e.m.f. due to inductance an e.m.f. 

 must be impressed on the circuit equal and opposite to 65. 



di 



= /oXsin (2 irft + 90) (curve 4). 



