Ohm's Law is such a fundamental concept that it comes into play virtually everywhere.
If you rearrange your Ep/Es = Is/Ip formula, you get:
Ep x Ip = Es x Is
As E x I gives you power (ignoring power factor), this is basically confirming that primary power = secondary power. In practice, of course, no transformer is 100% efficient, so secondary power will always be a little less than primary power.
I expect you're also familiar with the normal xfmr turns ratio formula:
Np / Ns = Ep / Es
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To clarify the original problem, current is directly proportional to voltage, so long as resistance remains constant. Increase the voltage and you will increase both the current and the power.
The inverse relationship applies if we are assuming constant power, as in the 60W bulb example above. If we increase the voltage, we need to decrease the current to keep the power the same. The only way to increase E and reduce I simultaneously is to increase the resistance.
[This message has been edited by pauluk (edited 06-20-2002).]
