How does an RL circuit behave when connected to an AC power source?

Inductive Reactance (XL):

When an AC power source is connected to the RL circuit, the alternating current flowing through the inductor induces a voltage across it. The inductor opposes changes in current, so it causes a phase shift between the voltage and current. The opposition to the flow of alternating current in an inductor is called inductive reactance (XL).

Phase Shift:

The voltage across the inductor lags the current flowing through it by 90 degrees in an ideal inductor (assuming there is no resistance in the inductor). This means that the voltage and current are out of phase in an RL circuit.

Impedance (Z):

The impedance of the RL circuit is the total opposition to the flow of AC current and is a combination of resistance and inductive reactance. The impedance (Z) can be calculated using the following formula:

Z = √(R² + XL²)

Current Lag:

Because of the phase shift, the current in the RL circuit lags the voltage across it. The larger the inductive reactance (XL), the greater the phase shift, and the more the current lags behind the voltage.

Voltage and Current Behavior:

As the AC voltage source alternates, the current in the RL circuit also alternates. However, the alternating current is affected by the inductive reactance, and its amplitude may differ from that of the voltage. The maximum current occurs slightly after the maximum voltage due to the phase shift.

Time Constant (τ):

The RL circuit has a characteristic time constant τ (tau) defined as the ratio of the inductance (L) to the resistance (R) in the circuit. It represents the time it takes for the current in the inductor to reach approximately 63.2% of its maximum value or decay to 36.8% during discharging.

AC Steady State:

In the steady state (after transient effects have diminished), the current and voltage oscillate in an RL circuit, but the current lags behind the voltage due to the inductive reactance. The circuit will reach a constant amplitude of current, and the phase relationship between voltage and current remains constant.

Overall, an RL circuit connected to an AC power source behaves as a low-pass filter, allowing low-frequency AC signals to pass more easily compared to higher frequencies. The behavior of the circuit is determined by the values of resistance (R) and inductance (L), as well as the frequency of the AC power source.