CURRENTS IN INDUCTIVE CIRCUITS. 27 



any current, i = /sin_p -f- (or E.M.F.) at that instant, since it 

 measures the displacement from its zero value. 



Two alternating currents i\ = I\ sin^ and i% / 2 sin (pt - 0) 

 have phases differing by an amount (or angle) 8, which is called 

 their Phase Difference. 



Equation (10) shows that in an inductive circuit the difference 

 of phase between the current and P.D. is given by 



PROBLEMS ON CHAPTER III. 



1. A straight conductor 1 metre long moves parallel to itself in simple 

 periodic motion of amplitude 1 centimetre at right angles to a uniform field of 

 strength 1000 C.G.S. units. If the periodic time is O'OOl second, what is the 

 maximum E.M.F. generated in the conductor? 



Answer. 6*28 volts. 



2. A circular conductor whose diameter is 1 metre revolves about a diameter 

 with an angular velocity of 10 revolutions per second in a uniform field of 

 strength 10,000 C.G.S. units, so that in one position of the conductor the lines 

 of force pass normally through it : what is the maximum E.M.F. developed ? 



Answer. 493'5 volts. 



3. A steady E.M.F. is applied between the terminals of a conductor whose 

 self-induction is 0'25 henry, and resistance 1 ohm : how long will it take the 

 current to reach one- tenth its steady value ? 



Answer. 0'025 second. 



4. What is the maximum value of the current in a conductor whose self- 

 induction is 0*5 henry, and resistance 2 ohms, when an alternating E.M.F., whose 

 maximum value is 100 volts, and frequency 100 cycles per second, is applied 

 between its terminals ? 



Answer. 0-3176 ampere. 



5. What is the impedance of the circuit in Question 4 ? 

 Answer. 314'2 ohms. 



6. What is the difference in phase between the E.M.F. and current in 

 Question 4? 



Answer. 86 20'. 



7. An alternator gives a potential difference between its brushes of 1000 

 volts when the current is 100 amperes ; if the current is increased to 150 amperes, 

 the external circuit being non-inductive, the potential difference falls to 920 volts. 

 What is the E.M.F. developed in the armature, the frequency being constant? 



Answer. 11 GO volts. 



8. What is the impedance of the armature in Question 7 ? 

 Answer. 1*6 ohms. 



9. What would be the potential difference between the brushes of the 

 machine in Question 7 if the current was increased to 175 amperes ? 



Answer. 880 volts. 



