31. Alternating Current

An AC circuit consists of an inductor and an emf source with frequency $0.25\mathrm{Hz}$. If the source is turned on at $t=0\mathrm{s}$, and the first time the voltage across the inductor reaches a maximum value is at $t=1.4\mathrm{s}$, when is the first time the current in the inductor is at a maximum?

A certain laptop charger says that the $V_{\text{rms}}$ provided to the laptop is 12 V. You know this charger is plugged into an outlet for which $V_{\text{rms}}$ is 120 V, such that there must be a transformer inside the laptop charger. If the number of windings of wire on the laptop side of the transformer is 60, how many windings of wire must be on the outlet side of the transformer?

The peak current to and from an inductor is i when the emf source has a peak voltage V and frequency f. What is the peak current to and from the inductor if the frequency and peak voltage are doubled to 2f and 2V$2\mathrm{V}$, respectively?

The peak current to and from an inductor is $I_{\mathrm{L}}$ when the emf source has a peak voltage $V$ and frequency $f$. What is the peak current to and from the inductor if the frequency and peak voltage are doubled to $2f$ and $2V$. respectively?