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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.
-Adding two 1,000 Ω resistors in series with R_L would be equivalent to:

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.
-Adding two 1,000 Ω resistors in series with R_L would be equivalent to:

Quizplus · Accepted Answer

11ecba2d_12f4_cb21_a3bf_9f95ffd31c43_MD0008_00 Electrical components in series are connected end to end, leaving only one path for the current to flow through the circuit. The properties of resistors in series are: The current through each resistor is the same. The voltage drop across each resistor is independent from that of the other resistors. The total voltage drop across all the resistors is equal to the sum of the individual voltage drops of the individual resistors. For resistors in series, the equivalent resistance is the sum of the individual resistances: 11ecba2d_12f4_cb22_a3bf_7fa449af5b8a_MD0008_00 The value of the resistor R_L is 1,000 Ω. If two resistors of 1,000 Ω are added in series with R_L, the equivalent resistance is the sum of all the individual resistances: 11ecba2d_12f4_cb23_a3bf_49c1f7d30a37_MD0008_00 Therefore, adding two 1,000 Ω resistors in series with R_L (also 1,000 Ω) is equivalent to multiplying R_L by 3. (Choice A) The equivalent resistance of a parallel circuit of resistors is calculated from: 11ecba2d_12f4_cb24_a3bf_adae379cbf89_MD0008_00 Using the above equation, the equivalent resistance for a parallel circuit is 11ecba2d_12f4_f235_a3bf_3f025fd9771d_MD0008_00 , which is the equivalent of multiplying R_L by 11ecba2d_12f4_f236_a3bf_89a044e402be_MD0008_00 (Choice B) Because the equivalent resistance of a series circuit of resistors is the sum of the individual resistances, the equivalent resistance cannot decrease. Educational objective: Circuit components in series are connected end to end and share the same current. The equivalent resistance of resistors in series is the sum of the individual resistances.

Passage Cable Theory Is a Mathematical Model Used to Calculate Currents