What is the term for the time required for the current in an RL circuit to build up to 63.2% of its maximum value?

In an RL (Resistor-Inductor) circuit, the time it takes for the current to rise to approximately 63.2% of its maximum value is known as one time constant. This time constant is represented by the symbol τ (tau), and it is calculated as the inductance (L) of the inductor divided by the resistance (R) in the circuit (τ = L/R).

During the initial moment after power is applied to an RL circuit, the current starts at zero and increases exponentially. One time constant represents the point in time when the current achieves the characteristic rise of this exponential function, reaching about 63.2% of its final steady-state value. This concept is fundamental in understanding how inductive circuits behave over time, particularly in relation to their transient response.

The other options represent different concepts. Two time constants would correspond to the current reaching about 86.5% of the maximum value, while three time constants would bring it to about 95%. Half-life, in a different context, typically relates to the time it takes for a quantity to reduce to half its initial value, which does not apply to the growth of current in an RL circuit.