After 5 time constants in the growth path of a DC series RL circuit, the current is at what level?

In a DC series RL circuit, the time constant is defined as the time it takes for the current to reach approximately 63.2% of its final value after a step change in voltage. The current in the circuit grows exponentially towards a maximum value, which is determined by the supply voltage and resistance in the circuit.

After one time constant, the current reaches about 63.2% of its maximum value, and after five time constants, the current will have reached over 99% of its maximum level. In practical terms, the growth of current is considered to be nearly complete at this point, and it is effectively at its maximum steady-state value.

Since the question refers to the current after five time constants, the current at this stage is indeed at its maximum level, as the exponential growth curve approaches its final steady-state value. This understanding is fundamental in the analysis of transient responses in electrical circuits, especially when dealing with inductors and resistors in series.