ELECTRIC MOMENTUM. INDUCTANCE. 157 



A 1 = h* + A," + 2A^ t cos 



Consider the energy A W in a small element of volume at the point /. This 

 energy is proportional to K* so that it may be considered in three parts which are 

 proportional to A^ 2 , to hf, and to hji^, respectively. But h l is proportional to 

 I v and A 3 is proportional to 7 2 , so that the kinetic energy in an element of volume 

 at the point p may be considered in three parts which are proportional respectively 

 to /! 2 , to /, 2 , and to I^I V What is true of the energy in an element of volume 

 at the point p is true of the energy in every other element of volume, that is, the 

 energy in every element of volume consists of three parts which are proportional 

 to /j s , to 7 2 2 , and to ./i/ 2 , respectively, so that the total energy consists of three 

 such parts. 



PROBLEMS. 



103. The current in a circuit has a value of 26 amperes at a 

 given instant. Three hundredths of a second later the current is 

 10.3 amperes. What is the average rate of change of the current 

 during the interval ? Is this rate positive or negative ? Ans. 

 523.3 amperes per second. 



104. Calculate the kinetic energy in joules of a current of 160 

 amperes in a circuit having an inductance of 0.05 henry. Ans. 

 640 joules. 



105. An electromotive force of 25 volts is connected to a cir- 

 cuit of which the resistance is 0.6 ohm and the inductance is 0.05 

 henry. At what rate is the current increasing : (a) At the instant 

 the electromotive force is connected to the circuit ; () at the 

 instant that the current reaches a value of 10 amperes, and (c) at 

 the instant that the current reaches a value of 3 5 amperes ? Ans. 

 (a] 500 amperes per second, (<) 380 amperes per second, (c) 80 

 amperes per second. 



106. The field winding of a dynamo has 50 ohms resistance 

 and, approximately, 7.5 henrys of inductance. Assuming that 

 the current grows in the coil in accordance with equation (52), 

 calculate the time required for the current in the winding to 

 reach 2 amperes when the winding is connected to a generator of 

 which the electromotive force is no volts. Ans. 0.359 second. 



107. A current has been left to die away in a circuit of 0.6 

 ohm resistance and 0.05 henry inductance. Find the rate of 



