MISCELLANEOUS EXAMPLES. 197 



9. A non-inductive resistance of 5 ohms is connected in parallel with a 

 resistanceless inductance of O'l henry, and with a capacity of 20 microfarads. 

 If the P.D. is 100 volts, what must be the frequency if the current in the main 

 circuit is (1) 20 amperes and (2) 40 amperes? 



Answers. (1) 112'5 periods per second. 



(2) 4*6 or 2761 periods per second. 



10. A non-inductive resistance of 10 ohms is placed in parallel with a resist- 

 anceless inductance, the P.D. being 100 volts, and the frequency 50 periods per 

 second. If the main current is 15 amperes, what is the value of the inductance ? 



Answer. 0-02847 henry. 



11. A non-inductive resistance of 5 ohms is placed in parallel with a con- 

 denser, the P.D. being 100 volts, and the frequency 100 periods per second. If 

 the main current is 21 amperes, what is the value of the capacity ? 



Ansiver. 102 microfarads. 



12. An inductance coil, whose resistance is 5 ohms, and a condenser circuit, 

 whose resistance is 10 ohms, are placed in series on a 50-frequency circuit: 

 the P.D. between the terminals of the condenser circuit is found to be 10 times 

 that between the terminals of the inductance coil. If the inductance is 0-01 henry, 

 what is the value of the capacity ? 



Answer. 54-8 microfarads, nearly. 



13. A 4-pole polyphase induction motor running on a 50-frequency circuit, 

 and at a maximum induction in the iron of 14,000 lines per square centimetre, 

 has, when running on full load, a slip of 5 per cent. The dimensions of the 

 stator are: internal diameter 10 inches, external diameter 16 inches, axial length 

 8 inches, and those of the rotor diameter 9j|^ inches, axial length 8 inches. 

 Allowing 15 per cent, for the insulation of the stampings, compare (1) the 

 hysteresis losses, (2) the eddy current losses, and (3) the total iron losses in the 

 stator and rotor respectively. 



Answers. (1) 8:1, nearly ; (2) 160 : 1, nearly ; (3) 116 : 1, nearly. 



14. The resistance of a coil of an armature is 7-5 x 10~ 5 , and its self-in- 

 duction is 0-000025 henry, and the current passing through it is 400 amperes. 

 As it passes under the brush a reversing E.M.F. of 2'5 volts is applied to it. 

 How long must the coil be short circuited before a reversal of current takes 

 place ?, 



Answer. 0'008 second. 



15. If a steady P.D. is applied between the terminals of a circuit whose 

 resistance is 5 ohms, and self-induction 0-005 henry, how long will it take for 

 the current to reach 0-75 of its steady value ? 



Answer. 0-001395 second. 



16. If four coils whose self-inductions are 0-1, O'Ol, 0-05, and 0-001 henry 

 respectively, and whose resistances are negligible, are connected in parallel, what 

 is the self-induction of the combination ? 



Answer. 0-000885 henry, nearly. 



17. If the coils in question 18 have resistances of 10, 1-5, and 0-1 ohms re- 

 spectively, what is (1) the equivalent resistance, (2) the equivalent self-induction, 

 (3) the impedance of the parallel arrangement, the frequency being 100 periods 

 per second ? Take v 2 = 10. 



Answers. (1) 0-011256 ohm ; (2) 0-000795 henry ; (3) 0'57 ohm nearly. 



