5.6:
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.
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.