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Illustration RL Circuit (Resistor, Coil)

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: \(U_{\text R} = R \, I(t)\).