# Illustration RL Circuit (Resistor, Coil)

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Here you can see the simplest RL circuit ever. It consists of a coil with inductance $$L$$ and a resistor $$R$$, both connected in series.

If an AC voltage $$U(t)$$ (e.g. sinusoidal voltage) is applied, which has the frequency $$f$$, then an AC current $$I(t)$$ flows through the circuit. At a finite frequency $$f \neq 0$$ (which would be a DC voltage), the coil has a resistance that opposes the change in current. This resistance is called inductive reactance $$X_{\text L}$$.

In a RL circuit, the current $$I(t)$$ lags the voltage $$U_{\text L}$$ across the coil by 90 degrees. Also the voltage $$U_{\text R}$$ at the resistor lags the coil voltage by 90 degrees, because $$U_{\text R}$$ is proportional to the current: $$U_{\text R} = R \, I(t)$$.