[Tex/LaTex] step-up and/or step-down transformer symbol for circuitikz

Question

I want to incorporate a more intuitive symbol for step up/down transformer in some of my drawings, such as the following:

or "cute inductor" version:

I tried to do what this link suggested; to copy the type of code used to define an "inductor" in pgfcircbipoles.tex ie, define a "long_inductor" to use in code like, but it isn't clear to me how to fit it all together:

\begin{circuitikz}
\draw (1,5) to[short, o-] (2, 5)
to [long_inductor, l = Primary] (2, 0)
to [short, -o](1,0);
\draw (2.3,5) -- (2.3,0);
\draw (2.4,5) -- (2.4,0);
\draw (4,4) to[short, o-] (3,4)
to [inductor,l = Secondary] (3,1)
to [short, -o](4,1);
\end{circuitikz}

I've seen examples using pstricks, but I only just started learning tikz and circuitikz so at this point I'm more interested in discovering how to use these tools… including, defining my own shapes for use.

Answer 1

The number of coils can be configured, also within a picture:

\begin{circuitikz}[]
\begin{scope}
   \ctikzset{bipoles/cuteinductor/width/.initial=1.2}%default 0.6
   \ctikzset{bipoles/cuteinductor/coils/.initial=10}%default 5
   \draw (0, 0)  to [short, o-] +(1, 0)
      to [cute inductor]  +(0, 3)
      to [short, -o] +(-1, 0);
\end{scope}
%% vertical bare fore the core.  The middle is in y=1.5
\draw[thick] (1.4, 0.5) -- (1.4, 2.5);
\draw[thick] (1.6, 0.5) -- (1.6, 2.5);
%% Secondary
\draw(3, 0)  to [short, o-] +(-1, 0)
  to [cute inductor]  +(0, 3) 
  to [short, -o] +(1, 0);
%%American inductor version(only working using the most recent gitversion!)
\begin{scope}[xshift=4cm]
\begin{scope}
   \ctikzset{bipoles/americaninductor/width/.initial=1.6}%default 0.8
   \ctikzset{bipoles/americaninductor/coils/.initial=8}%default 4
   \draw(0, 0)  to [short, o-] +(1, 0)
    to [inductor]  +(0, 3)
    to [short, -o] +(-1, 0);
\end{scope}
 %% vertical bare fore the core.  The middle is in y=1.5
 \draw[thick] (1.4, 0.5) -- (1.4, 2.5);
 \draw[thick] (1.6, 0.5) -- (1.6, 2.5);
%%Secondary    
\draw (3, 0)  to [short, o-] +(-1, 0)
 to [inductor]  +(0, 3)
 to [short, -o] +(1, 0);
 \end{scope}
\end{circuitikz}

While testing this, i found a bug, therefore, the code for the american inductor(not the cute/curly one)) is only working using the most recent git version or adjusting the code following this commit: https://github.com/circuitikz/circuitikz/commit/1dc2ee4cef798bcd8f9a5fabbaf83f66afeaf0f2

Best regards, Stefan