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Cable theory is a mathematical model used to calculate currents and voltages along and across axon membranes. The model treats small sections of the membrane as the resistor-capacitor circuit shown in Figure 1. An electric neuronal signal enters the circuit through the input node. A portion of the signal remains inside the axon and continues to the next section of membrane via Output 1, and the rest of the signal exits to the extracellular fluid via Output 2.
Figure 1 Circuit unit used to model axon membranesResearchers studied cable theory by recreating the circuit in Figure 1 using a 2 μF capacitor for C_M, a 200 Ω resistor for R_M, and a 1,000 Ω resistor for R_L. The researchers sent an electrical signal through the input and discovered that the capacitor acted as a resistor whose resistance varied with the signal's frequency, as shown in Figure 2.
Figure 2 Capacitor equivalent resistance vs. signal frequency for C_M
Adapted from Tuckwell H, Introduction to Theoretical Neurobiology 2006 SIAM.
- An ammeter is added to the circuit as shown. The voltage across the capacitor is kept constant while the frequency is increased from 200 Hz to 400 Hz. Through this change, the value shown by the ammeter:

Question

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Cable theory is a mathematical model used to calculate currents and voltages along and across axon membranes. The model treats small sections of the membrane as the resistor-capacitor circuit shown in Figure 1. An electric neuronal signal enters the circuit through the input node. A portion of the signal remains inside the axon and continues to the next section of membrane via Output 1, and the rest of the signal exits to the extracellular fluid via Output 2.

Figure 1 Circuit unit used to model axon membranesResearchers studied cable theory by recreating the circuit in Figure 1 using a 2 μF capacitor for C_M, a 200 Ω resistor for R_M, and a 1,000 Ω resistor for R_L. The researchers sent an electrical signal through the input and discovered that the capacitor acted as a resistor whose resistance varied with the signal's frequency, as shown in Figure 2.

Figure 2 Capacitor equivalent resistance vs. signal frequency for C_M
Adapted from Tuckwell H, Introduction to Theoretical Neurobiology 2006 SIAM.
-

An ammeter is added to the circuit as shown. The voltage across the capacitor is kept constant while the frequency is increased from 200 Hz to 400 Hz. Through this change, the value shown by the ammeter:

Quizplus · Accepted Answer

11ecba2d_12f4_55ee_a3bf_a7d0c22cd20a_MD0008_00 An ammeter in series with a circuit component measures the electric current flowing through it. In the given diagram, the ammeter is in series with the capacitor C_M, and therefore it measures the current through C_M. Ohm law states that the voltage V across an electrical component equals the product of its resistance R and the electric current I flowing through it (V = IR). Therefore, 11ecba2d_12f4_55ef_a3bf_adbc5a821f9a_MD0008_00 If V is fixed in the above equation, a change in R causes an inverse change in I. The capacitor's resistance R_C is found from Figure 2. At 200 Hz, the resistance R_C is 400 Ω, and it decreases to 200 Ω at 400 Hz. As such, decreasing R to half its value doubles I: 11ecba2d_12f4_55f0_a3bf_7bae361d954b_MD0008_00 Therefore, the current reading on the ammeter will double, or increase by 100%. (Choice A) If 400 Hz is incorrectly interpreted as the initial frequency value and 200 Hz as the final value, the resistance would appear to double and the current appear to decrease by 50%. (Choice B) If the ammeter is incorrectly assumed to measure voltage instead of current, the value shown by the ammeter would not appear to change because the voltage is kept constant. Educational objective: An ammeter in series with a circuit component measures the current through that component. Ohm law states that voltage equals the product of current and resistance: V = IR. Because current is inversely proportional to resistance if the voltage is fixed, reducing the resistance by half will double the current.

Passage Cable Theory Is a Mathematical Model Used to Calculate Currents