CURRENT VALUE. 91 



Exactly the same statement applies to an alternating 



electromotive force, the virtual voltage being 7 =^ of the 



V 2 

 maximum value. 



Scales of Instruments. Both ammeters and voltmeters 

 give readings proportional to the mean values of the square 

 of current or voltage, and would consequently give, in most 

 cases, a nearly even scale for (amperes)' 3 or (volts) 2 , the 

 amperes or volts being the virtual value of the current or 

 voltage. The reason for this is as follows : The reading 

 of all alternating-current measuring instruments is produced 

 either by the expansion of a heated wire or by the mutual 

 action of a fixed and a movable part. In hot-wire instruments 

 the average heating effect on the wire must obviously be due to 

 the average value of C* 2 R as explained above, and the expan- 

 sion of the wire is approximately proportional to the heat 

 given to it. In all other instruments the deflection depends 

 upon the force with which the fixed and movable parts act 

 upon one another. But both fixed and moving portions exert 

 forces proportional to the current or voltage being measured. 

 The resultant force depends, consequently, on the product 

 of the two forces exerted by the fixed and moving part, i.e., on 

 the product of two quantities, each separately proportional 

 to the quantity to be measured. It thus results that the 

 average force producing the deflection is the average of a 

 force due to (current x current) or (voltage x voltage), i.e., 

 to the average of the square of the quantity to be measured. 



As stated above, the scale of an alternating current 

 instrument would usually be evenly divided if graduated in 

 (amperes) 2 . 



An excellent example of this is the Siemens dynamometer, 

 in which the scale is uniformly divided, and the readings 

 give the values of the average value of (current) 2 . The 

 effective current is obtained by extracting the square root 

 of the reading. 



For convenience in reading, the scale of most instruments 

 is usually marked in volts instead of (volts) 2 . The scale of a 

 Cardew voltmeter would have divisions nearly equal in size 

 if its readings were proportional to (volts) 2 instead of volts. 



Thus it is seen that practically all direct-reading alter- 

 nating-current ammeters and voltmeters have an uneven 

 scale, since the distance between successive sub-divisions 



