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THE A C TRANSMISSION LINE 471
volts is consumed by the loss or drop in coil A. Therefore, neglecting the resistance of the connecting wires, 50 volts must be the drop across coil B. The circuit current is, by Ohm's Law (100 ~ 2000 ohms), 1/20 of an ampere. Then the power in coil B is 1/20 of an ampere times 50, or 2l/2 watts.
Now the reader may please himself by assigning other impedances to B and he will find that no impedance except that which equals the impedance of coil A will give him as much as 21/? watts in coil B. By trying one or two examples we will easily see the reason for this. Suppose we make B 500 ohms. Then the total impedance of the circuit is 1500 ohms and the current flowing is, by Ohm's Law, 100 divided by 1500, or 1/15 of an ampere. 1/15 of an ampere is a larger current than 1/20 of an ampere. We now have more current in coil B than before, but let us see about the power. Coil B now has only 1/3 of the total impedance of the circuit and .the voltage drop across it is only 33 1/3 volts. If the reader will apply elementary arithmetic to these figures he will find that the power in coil B is, now only 33 1/3 multiplied by 1/15, or 2 2/9 watts. The current flow through B has been increased but the voltage drop across coil B has been reduced, and the power in any resistor is the current flowing multiplied by the voltage drop.
If, on the contrary, we make B 2000 ohms, then there is a 66 2/3 volt drop across B. But the increased impedance has reduced the current flowing in the circuit to 1/30 of an ampere, and the power in B is again only 2 2/9 of a watt. The reader may make as many other calculations as he cares to, assigning any value of impedance whatever to coil B. He will invariably find that either the decreasing current in coil B or the decreased voltage drop across it reduces the power in that winding to some figure less than the 2*A watts obtained when the impedances were accurately matched.
(3) Impedance match is of great importance in sound systems, where the alternating currents representing speech are often extremely minute and any loss