PROBLEMS. 383 



17. Given a direct- reading ammeter (or voltmeter) of the alter- 

 nating-current type of which the actual length of a scale division 

 under the pointer is proportional to the reading of the pointer ; a 

 scale division being supposed to correspond to, say, o.i ampere 

 over the entire scale. The position of the pointer can be read to 

 a certain fraction of a degree of angle, so that the error in amperes 

 due to an error of reading is inversely proportional to the length 

 of the scale division under the pointer, that is, inversely propor- 

 tional to the reading of the pointer, (a) Find how many times 

 as great the error in amperes (due to an error in reading) is when 

 the instrument reads I ampere than when the instrument reads 

 10 amperes, (fr) Find how many times as great the percentage 

 error is in the first case than in the second case. Ans. (a) 10 

 times as great; (&) 100 times as great. 



Note. Ammeters and voltmeters which are suitable for direct-current circuits, only, 

 always give a deflection which is approximately proportional to the current or voltage. 

 Therefore the scales of direct-reading instruments of this type are scales of approxi- 

 mately equal parts. 



Ammeters and voltmeters which are suitable for both alternating and direct-current 

 circuits always give a deflection which is nearly proportional to the square of the cur- 

 rent or voltage. Let y be the deflection of such an instrument read on a scale of 

 equal parts, or, say in degrees, let dy be one of the divisions of this scale, and let x 

 be the current or voltage corresponding to the deflection y. Then 



y = kx* and dy = zkxdx 



where k is a constant. Now, in a direct-reading instrument each scale division corre- 

 sponds to a certain constant fraction part of an ampere or volt which may be repre- 

 sented by dx. Then the length of a scale division of such a direct-reading instrument 

 expressed in degrees is given by the value of dy, which, according to the above equa- 

 tion, is proportional to x y where x is the reading in amperes or volts of the direct- 

 reading instrument. 



Problems 15, 16, and 17 touch upon a matter of very great practical importance, 

 and two simple examples covering the entire ground may be worth while. A stand- 

 ardized direct-current ammeter (or voltmeter) which indicates 100 amperes (or volts) 

 with a certain degree of precision will indicate 50 amperes (or volts) with the same 

 actual error or with twice the percentage error. A standardized alternating-current 

 ammeter (or voltmeter) which indicates 100 amperes (or volts) with a certain degree 

 of precision will indicate 50 amperes (or volts) with twice as large an actual error or 

 with four times as large a percentage error. 



18. An ammeter indicates 6.2 amperes of alternating current 

 flowing through an arc lamp, a voltmeter indicates 82 volts across 



