SELF-INDUCTANCE 9 



and it is this resultant e.m.f. whicL maintains the current against 

 the resistance 7- of the circuit. Hence 



This equation may be written in the form 



the physical interpretation of which is, that the impressed e.m.f. at 

 any given instant may be regarded as employed in two ways : (1) in 

 balancing the drop of potential ri due to the resistance of the circuit ; 

 and (2) in balancing the opposing e.m.f. of self-inductance. 



Equation (1) is of great importance, and we shall frequently have 

 to make use of it. 



Let us now suppose that the practical units the volt, the ohm, 

 and the ampere are substituted for the C.G.S. units, and let us 

 choose the practical unit of self-inductance so that equation (1) will 

 also hold for the practical units, without being complicated by the 

 introduction of any constants. Let the practical unit of self-induc- 

 tance contain 10* C.G.S. units. In order to avoid unnecessary con- 

 stants, we must choose x so that 



Lx 10-xlO-=10. 



at at 



or x = 9, so that the corresponding practical unit of self-inductance, 

 termed the henry, is equal to 10 9 C.G.S. units. 



The corresponding practical unit of magnetic flux is equal to 10 8 

 C.G.S. units. [It has been proposed to call this unit of magnetic 

 flux a weber.] 



In some cases, the self-inductance of a circuit is so small as to be 

 practically negligible in comparison with its resistance. As an 

 example of such a circuit, we may consider an insulated wire which 

 has been doubled on itself and then wound into a coil as in the 

 usual method of winding standard resistance coils. Such a circuit is 

 termed a non-inductive one. An incandescent lamp whose resistance 

 is very high and self-inductance very low is another example of a 

 non-inductive circuit. 



6. Sine Waves in Circuits containing Resistance, 

 Self -inductance, and Capacity 



Consider a non-inductive circuit of resistance r in which there is 

 an alternating current represented by 



i = I sin pt ........ (2) 



