5.6: Design Example: Frog Muscle Response
A student is tasked to work on an intriguing experiment involving an RL (Resistor-Inductor) circuit to study the muscle response of a frog's leg to electrical stimulation. The RL circuit plays a crucial role in this experiment, providing the means to control and measure the electrical impulses that trigger muscle contraction.
When the switch connecting the RL circuit is closed, a brief muscle contraction is observed. This is because, at a steady state, the inductor acts like a short circuit, bypassing the resistor and causing a mild, brief contraction in the frog's leg. Applying Ohm's law to the 60-ohm resistor, the student can calculate the initial current passing through the circuit.
Upon opening the switch, the RL circuit becomes source-free. Now, the current flows through the resistor, which the student models as the frog's leg. This change causes sustained muscle activity lasting for ten seconds.
The student assumes that a current of 20 milliamperes is responsible for inducing this sustained muscle response. To verify this assumption, they use the time constant of the RL circuit, which equals the ratio of inductance to resistance. The current passing through the inductor can be expressed using the calculated initial current and this time constant.
Substituting the current and time values corresponding to the sustained muscle activity into the current equation, the student can solve for the unknown resistance. This resistance value represents the modeled resistance of the frog's leg.
This experiment serves as a practical demonstration of how RL circuits can be used to study physiological responses. It illustrates the fundamental principles governing these circuits, such as transient and steady-state responses and the concept of the time constant. By drawing parallels between electrical circuits and biological systems, it also highlights the interdisciplinary nature of science, bridging the gap between physics and biology.
