ALTERNATING CURRENTS 



JIir-INDUCTANCt E.fl.F. 



and is not much used commercially, most modern forms being 

 indicating instruments, in which the fine-wire coil is allowed to 

 move, a suitable spring furnishing the controlling couple. Now, as 

 soon as the fine- wire coil is displaced from its position at right angles 

 to the main coil, there is, on account of the mutual inductance 

 between the coils, an e.m.f. induced in it, and this e.m.f. is a variable 

 one, depending on the relative positions of the two coils. Thus a 

 further possible source of error arises in connection with indicating 

 instruments. 



In order to investigate this error, we may conveniently use a 

 diagram similar to that of Fig. 32. With no mutual inductance 



between the coils, the reading 

 would be proportional to V 

 in Fig. 34. Owing to mutual 

 inductance, the e.m.f. V m due 

 to it must be compounded 

 with V, and the resultant 

 treated as if it represented 

 the p.d. impressed on the 

 fine-wire circuit. It is thus 

 evident that the reading will 

 be proportional to V m '. Now, 

 in the perfect instrument the 

 reading would be proportional 

 to V, so that the error when 

 mutual inductance is taken 

 into account is proportional 

 to V m ' - V. With no mutual 

 inductance present, the error 

 would be proportional to 

 V/ V, i.e. in the case 

 shown in the diagram it 

 would be greater. Thus mutual inductance, in the case shown, has 

 the effect of redwing the error due to self-inductance.* It is easy 

 to see that for negative values of 0, i.e. for leading currents, the 

 error due to self-inductance would be increased by mutual inductance. 

 If, however, the self-inductance and capacity effects are quite 

 negligible, then it is evident from the diagram that (V = V m ' = V r ') 

 mutual inductance does not introduce any error. 



We may summarize the above results by saying that mutual 

 inductance tends to correct the errors of a wattmeter so long as the 

 current is a lagging one, and to exaggerate the errors if the current 

 is a leading one. 



* Or capacity, or self-inductance and capacity combined. 



FIG. 34. To illustrate Effect of Mutual Induct- 

 ance. 



