= RL low-pass filter
{c}
{title2=$H(\omega)=R/(R+i\omega L)$}
An <RL circuit> with the output measured across its <resistor> is a first-order <low-pass filter>. For an ideal <inductor>, an ideal voltage source and a high-resistance output instrument, the <electrical impedances> $i\omega L$ and $R$ give
$$
H(\omega)=\frac{R}{R+i\omega L},\qquad |H|=\frac{1}{\sqrt{1+(\omega L/R)^2}},\qquad \omega_c=\frac RL.
$$
The gain approaches one at low <angular frequency> and $R/(\omega L)$ at high <angular frequency>; at $\omega_c$ it is $1/\sqrt2$. The time-domain equation is $L\dot I+RI=V_{\rm in}$ and $V_{\rm out}=RI$, so the <time constant> is $L/R$. Instrument loading, source resistance and nonideal <inductance> can change the response.
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