The good news is that you can specify the number of coils with the american inductor and the cute inductor. The bad news is that there is a bug in the american inductor code.
\documentclass{standalone}
\usepackage{circuitikz}
\ctikzset{bipoles/cuteinductor/coils=3}
\ctikzset{bipoles/americaninductor/coils=3}
\ctikzset{bipoles/vcuteinductor/coils=3}% variable
\ctikzset{bipoles/vamericaninductor/coils=3}
\begin{document}
\begin{circuitikz}
\draw (0,0) to[cute inductor] (2,0)
(0,1) to[american inductor] (2,1)
(0,2) to[variable cute inductor] (2,2)
(0,3) to[variable american inductor] (2,3);
\end{circuitikz}
\end{document}

Here is the bug fix for the american inductor:
\makeatletter
%% american inductor
\pgfcircdeclarebipole{}{\ctikzvalof{bipoles/americaninductor/height 2}}{americaninductor}{\ctikzvalof{bipoles/americaninductor/height}}{\ctikzvalof{bipoles/americaninductor/width}}{
\pgf@circ@res@step=\ctikzvalof{bipoles/americaninductor/width}\pgf@circ@Rlen
\pgfsetlinewidth{\pgfkeysvalueof{/tikz/circuitikz/bipoles/thickness}\pgfstartlinewidth}
\pgftransformationadjustments
\advance \pgf@circ@res@step by \pgfhorizontaltransformationadjustment\pgflinewidth
\divide \pgf@circ@res@step by \ctikzvalof{bipoles/americaninductor/coils}
\divide \pgf@circ@res@step by 2
\pgf@circ@res@other = \ctikzvalof{bipoles/americaninductor/coil height}\pgf@circ@Rlen
\pgfpathmoveto{\pgfpoint{\pgf@circ@res@left-\pgfhorizontaltransformationadjustment*0.5*\pgflinewidth}{-\pgfverticaltransformationadjustment*0.4*\pgfstartlinewidth}}%correct value would be 0.5 but arcs are not really flat, therefore 0.4 is better is (almost) all cases
\foreach \x in {1,...,\ctikzvalof{bipoles/americaninductor/coils}}
{\pgfpatharc{180}{0}{\pgf@circ@res@step and \pgf@circ@res@other}}
\pgfsetbuttcap
\pgfsetbeveljoin
\pgfusepath{stroke}
}
\makeatother
circuitikz
(Version 0.8 (2017-03-08)). There are some novelties also for inductors.