MEASUREMENT OF POWEtt. 187 



back to its original position, with its plane normal to that of the 

 thick coil, by means of the torsion head. The angle through 

 which the torsion head has to be rotated is proportional to the 

 couple necessary to balance the couple due to the mutual action 

 of the two currents, hence 



(1) 



where ^ is the current in the thick coil and i that in the thin coil 

 and c is a constant. 



If the thin coil is non-inductive 



e = ri ........ (2) 



where r is its resistance, so that is proportional to eii, that is to 

 the power given to the circuit. If, however, the thin coil is 

 inductive, a correction has to be applied, since then the current i 

 is not in phase with the potential difference between its terminals, 

 and is also less than it would be if it were non-inductive. 



We proceed to determine this correcting factor. 



131. Determination of the Correction Factor 

 of a Wattmeter. Let Zi, n, ii be respectively the self- 

 induction, resistance, and E.M.S. current of the circuit, the 

 power given to which is to be measured, and let L, r, i be 

 respectively the self-induction resistance, and E.M.S. current 

 of the thin coil of the wattmeter, also let p = 2ir)i, where n is 

 the frequency of the supply current, and e the E.M.S. potential 

 difference between the common terminals of the two circuits. 



Then using vector methods 



+ 



and 



Now, the true power given to the circuit is the scalar product 

 of ii and e, that is 



power = * f/W a (?>) 



