= Periodically switched RL circuit
{title2=$I_{\max}=(V/R)/(1+e^{-R\Delta t/L})$}
An <RL circuit> alternating for equal intervals $\Delta t$ between zero drive and constant drive $V$ has a unique attracting periodic <electric current> when $R,L,\Delta t>0$. Write $s=e^{-R\Delta t/L}$ and $J=V/R$. Sampling just before each zero-drive interval gives the <recurrence relation> $I_{n+1}=s^2I_n+J(1-s)$. Subtracting its <fixed point> yields $I_n-J/(1+s)=s^{2n}[I_0-J/(1+s)]$. Thus the limiting upper and lower <electric currents> are $J/(1+s)$ and $sJ/(1+s)$; convergence is geometric. This gives a simple exact ripple estimate for a periodically driven <inductor>.
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