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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.
-At 200 Hz, the current in C_M is 0.7 A. What is the current in R_M?

Question

Passage
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.
-At 200 Hz, the current in C_M is 0.7 A. What is the current in R_M?

Quizplus · Accepted Answer

11ecba2d_12f2_cf3c_a3bf_43e0bbdffefe_MD0008_00 Circuit components in parallel are connected to each other at both ends and have the same voltage across them. 11ecba2d_12f2_cf3d_a3bf_6111f8625679_MD0008_00 Ohm law states that the voltage across a resistor equals the product of its resistance and the current flowing through it (V = IR). Because R_C and R_M are connected in parallel, the product of their currents and resistances must be equal: 11ecba2d_12f2_cf3e_a3bf_b731077b21da_MD0008_00 The current I_M through the resistor is obtained by dividing both sides of the equation by R_M: 11ecba2d_12f2_cf3f_a3bf_25261076a320_MD0008_00 The capacitor's resistance R_C is found from Figure 2. At 200 Hz, the capacitor's resistance R_C = 400 Ω. The current through the capacitor is given as I_C = 0.7 A, and the resistor's resistance is given as R_M = 200 Ω. Therefore, the current through the resistor can be calculated: 11ecba2d_12f2_cf40_a3bf_33501eaabe22_MD0008_00 (Choice A) Because the voltages of parallel resistors are equal, current and resistance are inversely proportional (V = IR). Resistors R_C and R_M have the same voltage across them, and therefore the larger of the two resistors will have the smaller current. (Choice B) Resistors in parallel have the same current only if they have the same resistance. Educational objective: Circuit components in parallel have the same voltage across them. The current through a resistor can be determined from its resistance and the voltage across it using Ohm law: V = IR.

Passage Cable Theory Is a Mathematical Model Used to Calculate Currents