Design Example: Frog Muscle Response

A student uses an RL circuit to study the muscle response of a frog's leg to electrical stimulation.

Closing the switch causes a brief muscle contraction while opening it triggers sustained muscle activity for 0.01 seconds.

The student models the frog's leg as a resistor to determine its resistance, assuming that a current of 20 milliamperes induces the sustained muscle response.

When the switch is closed, the inductor acts as a short circuit at a steady state, bypassing the resistor and causing a mild muscle contraction.

Applying Ohm's law to the 60 ohm resistor gives the initial current.

When the switch is opened, the circuit becomes a source-free RL circuit. Current now flows through the resistor, causing sustained muscle activity.

The time constant equals the ratio of inductance to resistance, and the current passing through the inductor is expressed using the calculated initial current and time constant.

The current and time values corresponding to the sustained muscle activity are substituted into the current equation. Solving the equation gives the value of the unknown resistance.