How does an RL circuit reach its steady-state condition?

During the initial energization or when there is a change in the input voltage, the RL circuit behaves transiently before reaching the steady state. The behavior of an RL circuit can be divided into two phases:

Transient Phase: When the circuit is first energized or when there is a sudden change in input voltage, the inductor opposes the change in current flow. According to Faraday's law of electromagnetic induction, an inductor generates a back EMF (Electromotive Force) that opposes the change in current. As a result, the current in the circuit starts to rise gradually.

The rate of rise of current (di/dt) is proportional to the applied voltage and inversely proportional to the inductance (L) and resistance (R) of the circuit.

During this phase, the voltage across the inductor is relatively high, and the voltage across the resistor is relatively low.

Steady-State Phase: As time passes, the inductor's back EMF weakens, and the current starts to reach its maximum value, stabilizing to a constant value. This is the steady-state condition of the RL circuit.

In the steady state, the inductor acts as a short circuit to direct current (DC), so its impedance is effectively zero.

At steady state, the voltage drop across the inductor is zero (since it acts as a short circuit), and the voltage drop across the resistor is the entire applied voltage.

The time it takes for the RL circuit to reach the steady-state condition depends on the time constant (τ) of the circuit, which is given by the formula τ = L / R. The time constant represents the time it takes for the current to reach approximately 63.2% of its steady-state value. After about 5 time constants (5τ), the current is considered to have reached its steady-state condition.

In summary, an RL circuit reaches its steady-state condition as the current stabilizes to a constant value over time due to the inductor's behavior and the interaction with the resistor in the circuit.