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How to compute RL current fall time in Python using UliEngineering

You can easily compute the RL current fall time to reach a target current using the UliEngineering Python library:

rl_current_fall_time.py
from UliEngineering.Electronics.RL import rl_current_fall_time
from UliEngineering.EngineerIO import *

# Compute time to fall to 10% of initial current
time = rl_current_fall_time("10", "100mH", 0.10)
print(f"Time to 10% current (10Ω, 100mH): {format_value(time, 's')}")

# Compute time to fall to 1% of initial current
time = rl_current_fall_time("1k", "1mH", 0.01)
print(f"Time to 1% current (1kΩ, 1mH): {format_value(time, 's')}")

Example output

rl_current_fall_time_output.txt
Time to 10% current (10Ω, 100mH): 23.0 ms
Time to 1% current (1kΩ, 1mH): 4.61 µs

The RL current fall time represents the time required for current through an inductor to decay to a specific percentage of its initial value when the voltage source is removed. This calculation is essential for understanding relay release times, inductive load switching safety, and the transient response of RL networks. The current decay follows an exponential curve, with the current never truly reaching zero in finite time.

The fall time is computed using the formula: $t = -\tau \ln(\text{ratio})$, where $\tau = \frac{L}{R}$ is the time constant and the ratio is the target current as a fraction of the initial current (e.g., 0.10 for 10%). For example, falling to 10% of initial current takes approximately 2.3 time constants, while falling to 1% takes approximately 4.6 time constants.

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