20 ELECTROMOTIVE FORCE AND CURRENT. 



He should carefully work the following examples, and, 

 if necessary, read again the foregoing pages. 



Example. A circuit has a resistance of -5 ohm., and a 

 self-induction of 20 milli-hemies. It carries an alternating 

 current whose maximum value is 24 amperes. Plot curves 

 on squared paper to represent the following quantities : 



(a) The current, (b) The rate of change of current. 

 On a separate sheet plot the following electromotive forces 

 making use of the curves (a) and (6) : (c) Electromotive 

 force necessary to overcome resistance, (d) Electromotive 

 force necessary to overcome self-induction. From (c) and 

 (d) obtain the curve (e) representing the total electromotive 

 force necessary to maintain the current. 



Caution*. It may not be out of place to mention one or 

 two points which frequently cause confusion at first in con- 

 nection with curves similar to those just discussed. 



(1) A curve displaced towards the right is later in phase. 

 This is the contrary of what one might expect on con- 

 sidering the matter carelessly, but is at once evident from 

 the construction given at first for obtaining the curve. 



(2) In commencing the drawing of a curve a little 

 consideration is required to ascertain whether its maximum 

 value should be measured above or below the horizontal. 

 If the quantity upon which the curve is dependent is 

 decreasing in value, the maximum value of the curve must 

 be above the line, so that succeeding points on it may be 

 lower, and vice versa. 



(3) The voltage supplied to a circuit is opposite in direction 

 to the voltages set up in the circuit due to resistance or self- 

 induction. This may appear obvious, but neglect of this 

 distinction will cause confusion. In diagrams Figs. 6 and 7 

 the electromotive forces shown are those supplied from the 

 external source to the circuit, and not those set up in the 

 circuit, since they are on the same side of the horizontal 

 axis, .and therefore in the same direction, as the current, 

 whereas the opposing voltages must obviously be in the 

 opposite direction, i.e., on the opposite side of the zero line. 



Thus the curve marked E,. in Fig. 7 is the voltage over- 

 coming (and, therefore, oppositely directed to) the voltage 

 C R of the circuit opposing the flow of current. The latter 

 might be represented by a similar curve to E r at equal 

 distances on the opposite side of the base line. 



