I recently came across a question, for which I saw two possible methods of finding the solution. I was required to calculate the "current flowing" $I$ when given the voltage $V$, frequency $f$, total resistance $R$ and impedance of the circuit $Z$. In the book that these questions were written, there were two methods (Note - AC Current):
First Method:
$$V=|I\cdot Z|\ \Longrightarrow\ \frac{V}{|Z|}=|I|$$
Second Method:
$$V=I\cdot R\ \Longrightarrow\ \frac{V}{R}=I$$
(I use all the time for DC Currents)
As I found out, through trial and error, both of these give different solutions. Personally, I tended towards the first solution, but I couldn't help noticing the second method, as it gave a nice round answer, as opposed to the fractional answer the first gave. Which of these two methods is the correct one to use?