FUNDAMENTAL PROBLEMS. 77 



A careful consideration of this mechanical analog will serve to 

 elucidate one of the most important aspects of electrical reson- 

 ance. Suppose that the mechanical resistance of the water in 

 Fig. 67 is not very large, then a very small alternating force / 

 applied to the system shown in Fig. 67 will, if it continues to act 

 for some time, build up a very violent oscillatory motion, and the 

 spring will be subjected to bending forces vastly greater than the 

 maximum value of the force/. In fact the spring may be broken 

 by the continued application of a comparatively weak alternating 

 force of the proper frequency. Similarly, a weak alternating 

 electromotive force of the critical frequency applied to the circuit 

 shown in Fig. 57 will, if it continues to act for some time, build 

 up a very large alternating current, and the electromotive force 

 across the condenser terminals (= l~/a>C) may become so large 

 as to break through the insulation of the condenser. 



35. Multiplication of electromotive force by resonance. When 

 resonance exists in a circuit containing a condenser and an induc- 

 tance in series, the effective electromotive force, coLf, across the 

 terminals of the inductance and the effective electromotive force 

 f/coC across the terminals of the condenser may both be much 

 greater than the effective electromotive force RI which acts on 

 the circuit. This fact is easily understood by referring to the 

 mechanical analog. Thus, if a periodic force acts on a weight 

 which is suspended by a helical spring, the weight will be set into 

 very violent oscillation even if the periodic force is weak, provided 

 the frequency of the force is the same as the frequency of free 

 oscillation of the weight. Under these conditions the force which 

 alternately stretches and compresses the spring, and the force 

 which accelerates the weight up and down may both be enorm- 

 ously greater than the periodic force which acts on the system 

 from outside. 



Example. Under the conditions specified in connection with 

 Fig. 66, namely, R 2 ohms, L = 0.352 henry, and C= 20 

 X io~ 6 farad, the electromotive force of 200 volts at the critical 



