TESTS OF TRANSFORMERS. 109 



4. Show that, taking leakage into account, the condition in Question 3 is 

 obtained by writing 



L^L 2 for M 



where L l is the self-induction of the primary coil, and L 2 that of the secondary 

 coil. 



5. A condenser of capacity C is permanently connected in parallel with the 

 primary coil of a transformer : show that the power factor will be unity, if 



G = WT^? 



where 



the notation being as in Question 3. 



6. Tn a transformer having no magnetic leakage the self-inductions of the 

 primary and secondary coils are respectively 1 and O'l henry, the resistances 

 10 ohms and O'l ohm, the mutual induction of the two coils 0'09, and the fre- 

 quency 100 periods per second : what capacity must be placed in parallel with 

 the primary coil to give unit power factor ? 



Answer. About 2*8 microfarads. 



7. A transformer has a primary and two secondary coils ; the resistance and 

 self-induction of the primary are 10 ohms and O'OOl henry respectively ; those 

 of the first secondary are 5 ohms and 0'0005 henry respectively, and those of the 

 second secondary are 1 ohm and O'OOOl henry respectively ; the mutual induc- 

 tions between the primary and first secondary, the primary and second second- 

 aries, and the two secondaries, are respectively 0'00065, 0*0003, and 0002 

 henry. If the primary P.D. is 1000 volts, what is the primary current, and what 

 is the difference of phase between P.D. and current, the frequency being 100? 



Answer. 98'52 amperes; 6 10'. 



8. The P.D. between the primary terminals of a transformer is 2000 volts, 

 the current is 0*15 ampere, and the power as measured by a wattmeter is 275 

 watts : what is the power factor ? 



Answer. 91*67 per cent. 



9. Show that, if the resistance of the secondary coil of a transformer is negli- 

 gible, its efficiency is a maximum when the external secondary resistance is 

 numerically equal to the total reactance of the secondary circuit. 



