Which of these two methods is correct for calculating current?

Question

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?

Answer 1

Method 1 is universal, method 2 works only for dc.

Method 2 is for DC supply, whereas the Method 1 is for AC supply.In AC circuit the Inductor (a coil) and a capacitor pose resistance which is calculated as impedence of circuit. .

Whereas in DC , capacitor fully blocks the supply and thus capacitive reactance is infinite and the inductive reactance is zero. thus the current in a capacitive circuit is zero. z^2=R^2 + (xl -xc )^2 ; z(dc)=R; Also the difference of Xl and Xc is small and thus answer is approximately the same by the method 2 in AC circuits too.