Design Example: Frog Muscle Response

When the switch closes, the inductor acts as a short circuit at steady state, bypassing the resistor. This causes a mild, brief muscle contraction in the frog's leg. The inductor's behavior changes over time as current reaches steady state, fundamentally affecting circuit response.

Opening the switch converts the RL circuit into a source-free RL circuit. Current now flows through the resistor, modeling the frog's leg, causing sustained muscle activity lasting approximately 10 seconds. This transient response demonstrates how energy stored in the inductor dissipates through resistance.

The time constant equals the ratio of inductance to resistance and determines how quickly current decays in a source-free RL circuit. It characterizes the sustained muscle response duration and allows calculation of current at any time. This parameter is essential for predicting physiological responses to electrical stimulation.

Applying Ohm's law to the 60-ohm resistor yields the initial current when the switch closes. The voltage across the resistor divided by its resistance gives the current value. This calculation provides the baseline for analyzing how current changes during transient and steady-state conditions.

The student assumes 20 milliamperes induces sustained muscle activity based on experimental observation. This threshold represents the minimum current needed to trigger the physiological response lasting approximately 10 seconds. Using this assumption with the current decay equation allows solving for the unknown resistance modeling the frog's leg.

Modeling the frog's leg as a resistor simplifies the biological system into an electrical component. By substituting known current and time values into the exponential current decay equation, the student can solve for this unknown resistance. This approach bridges electrical circuit theory with physiological response, demonstrating interdisciplinary problem-solving.

Closing the switch produces a brief, mild contraction because the inductor bypasses the resistor at steady state. Opening the switch triggers sustained muscle activity lasting 10 seconds as current decays through the resistor. This contrast illustrates transient versus steady-state responses in first-order circuits.