Compare the behavior of an RL circuit in a DC circuit versus an AC circuit.

DC Circuit:

In a DC circuit, a constant voltage is applied across the RL circuit. When the circuit is initially energized, the inductor opposes the change in current, and as a result, it takes some time to build up the current to its maximum value. The inductor behaves like an open circuit when it is charging up, offering high impedance to the flow of current. Eventually, the current stabilizes, and the inductor behaves like a short circuit.

Once the circuit reaches a steady state, the inductor acts as a short circuit for DC, and the behavior becomes similar to a purely resistive circuit. At this point, Ohm's law applies, and the current through the circuit is given by I = V / R, where V is the applied voltage and R is the resistance of the resistor. The inductor essentially has no effect on the current in a DC circuit after the initial transient.

AC Circuit:

In an AC circuit, a sinusoidal voltage is applied across the RL circuit. As the voltage alternates, the current through the inductor also changes. However, inductors resist changes in current, so they create a phase shift between the voltage and current.

When the voltage is at its maximum (peak) value, the current through the inductor is at its minimum, and vice versa. This is because when the voltage is rising, the inductor resists the change in current, causing a lag in the current. Similarly, when the voltage is falling, the inductor tries to maintain the current, causing it to lag behind the voltage.

The current lags the voltage in an RL circuit by a phase angle φ, where the tangent of φ is given by ωL / R, with ω being the angular frequency of the AC source. This phase shift is present as long as there is an AC voltage applied, and it makes the behavior of the RL circuit different from a purely resistive circuit.

In summary, the main difference between the behavior of an RL circuit in a DC circuit and an AC circuit lies in the transient response and the presence of a phase shift between voltage and current in the AC circuit. In DC, the inductor is effectively bypassed after the initial transient, while in AC, the inductor causes a phase difference between voltage and current, affecting the circuit's impedance and reactance.