THE TRANSFORMER 277 



it is seen that any change in voltage must be accompanied 

 by a change in current in the opposite sense. 



Equations (69), (72), and (73) give only the approximate 

 relations of the transformer quantities; the derivation of 

 the exact relations requires us to consider the loss due 

 to hysteresis and eddy currents in the core, the PR losses 

 in the windings, and the magnetic leakage. 



69. Commercial Importance of the Transformer. From 

 the previous simple analysis it is seen that, by means of a 

 transformer a-c. power may be changed from one voltage 

 to another; if the secondary coil has more turns than 

 the primary, the voltage will be raised (i.e., " stepped up ") 

 and if the secondary coil has fewer turns the voltage will 

 be lowered ("stepped down"). Some of the greatest 

 power developments to-day are hydro-electric (using water 

 turbines for prime movers) in which the power station 

 must be situated close to the falls, the power of which is 

 being used. The place where the electric power is con- 

 sumed may be a hundred miles or more distant, so that a 

 long distance transmission line is necessary to carry the 

 power to the place of consumption. 



Long Distance Transmission Requires a High Voltage. 

 It is commercially impossible to carry electric power any 

 great distance unless high voltage is used, because of the 

 high I 2 R losses in the line, or else the heavy investment 

 for the copper wires. An approximate rule for the voltage 

 of ordinary transmission lines is from 500 to 1000 volts 

 per mile length of the line. A line 150 miles long might 

 be run at 80,000 volts or 100,000 volts, although special 

 conditions may cause departure from this rule. 



Location of Transformer in a Power-transmission System. 

 These high voltages cannot be generated directly in an 

 alternator, neither can the power be supplied to the con- 

 sumer at such a high voltage, hence the problem the elec- 

 trical engineer has to face is this: The power may be 

 generated at medium voltages (2300-11,000 volts), must 



