In a circuit containing resistance and inductance, the time required for current to reach its full value involves which of the following calculations?

The time required for current to reach its full value in a circuit that contains resistance and inductance is calculated using the formula derived from the time constant of an RL (resistor-inductor) circuit, which is represented as L/R.

In an RL circuit, the behavior of current flow as it ramps up to its maximum value is governed by the inductance (L) and the resistance (R) in the circuit. Specifically, the time constant indicates how quickly the current approaches its final steady state. It can be understood as the time it takes for the current to rise to approximately 63.2% of its final value. After a duration of about five time constants (5L/R), the current is considered to have reached a value extremely close to its maximum.

This relationship is essential for understanding transient responses in circuits and how quickly they react to changes, such as when a voltage is suddenly applied or removed. The formula directly reflects the interaction between the inductive and resistive elements, showing that higher inductance or higher resistance will slow the rate at which the current builds up.

Other calculations listed, such as V/I, represent simple Ohm’s law for resistance and would not apply to the transient response in an RL circuit. C/R