How Does a Nerve Cell Membrane Model Circuit Behave?

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In summary, the conversation is about a homework problem involving a simple model of a nerve cell membrane. The model includes two batteries with different voltages, two resistors representing resistance, and a switch for variability. The questions involve the voltage difference across the membrane, current flow, and voltage drops across the resistors. The conversation also touches on the possibility of different voltages if the locations of the resistors were reversed.
  • #1
muscles00gt
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Sorry if this is in the wrong area, but I'm having a bit of difficulty on one of my homework problems.

A simple model of the membrane of a nerve cell is shown in the figure at the right (seen below). It consists of 2 batteries (ion pumps) with voltages V1=100mV and V2=50mV. The resistance to flow across the membrane is represented by two resistors with resistances R1=10KΩ and R2=90KΩ. The variability is represented by a switch, SW1. Four points are labeled by the letters a-d. Point b represents outside of membrane and point d inside the membrane.

Picture of circuit:
PhysicsCircuit.jpg


A) What is the voltage difference across the membrane when the switch is open?

B) What is the current flowing around the loop when the switch is closed?

C) What is the voltage drop across the resistor R1 when switch is open? closed?

D) What is the voltage drop across the resistor R2 when switch is open? closed?

E) What is the voltage difference across the membrane when switch is closed?

F) If the locations of resistance R1 and R2 were reversed, would the voltages across the cell membranes be different?
 
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  • #2
so what are your thoughts abouit this, and what do you know?

One battery is probably the Potassium gradient (have you learned about Nernst potentials?) while the other is tied to the Na gradient. the switch is the fact that the sodium channels are normally closed, but if raised to a certain potential within a certain time window, will open (opposite the convention for switch terminology) and the transmembrane potential shoots up from say a -70mV resting state to +40mV
 
  • #3


I would be happy to help you with your homework problem! Here are the answers to the questions:

A) When the switch is open, no current is flowing through the circuit, so the voltage difference across the membrane is 0V.

B) When the switch is closed, the current flowing around the loop is V1/R1 + V2/R2 = (100mV/10KΩ) + (50mV/90KΩ) = 0.01mA + 0.000556mA = 0.010556mA.

C) When the switch is open, no current is flowing through R1, so the voltage drop across it is 0V. When the switch is closed, the voltage drop across R1 is (0.01mA)(10KΩ) = 0.1V.

D) When the switch is open, no current is flowing through R2, so the voltage drop across it is 0V. When the switch is closed, the voltage drop across R2 is (0.000556mA)(90KΩ) = 0.05V.

E) When the switch is closed, the voltage difference across the membrane is V1 - V2 = 100mV - 50mV = 50mV.

F) If the locations of resistance R1 and R2 were reversed, the voltages across the cell membranes would be different because the current flows in different paths in the circuit. This would result in a different voltage drop across each resistor and therefore a different voltage difference across the membrane.
 

1. What are the basic components of a circuit?

The basic components of a circuit are a power source, conductors, resistors, and loads. The power source supplies energy to the circuit, conductors carry the current, resistors limit the flow of current, and loads are devices that use the current to do work.

2. How do you calculate the total resistance in a series circuit?

In a series circuit, the total resistance is equal to the sum of all the individual resistances. This can be calculated using the formula R = R1 + R2 + R3 + ... where R is the total resistance and R1, R2, R3, etc. are the individual resistances.

3. What is the difference between a series circuit and a parallel circuit?

In a series circuit, the components are connected in a single loop and the current flows through each component in order. In a parallel circuit, the components are connected in multiple branches and the current splits between the branches. In a series circuit, the total resistance is equal to the sum of the individual resistances, while in a parallel circuit, the total resistance is less than the smallest individual resistance.

4. How do you calculate the current in a circuit?

The current in a circuit can be calculated using Ohm's law, which states that current (I) is equal to voltage (V) divided by resistance (R). This can be written as I = V/R. Additionally, the current can be calculated by dividing the total voltage of the circuit by the total resistance.

5. What is the difference between AC and DC circuits?

AC (alternating current) circuits have a changing current and voltage, while DC (direct current) circuits have a constant current and voltage. AC circuits are used for long distance power transmission, while DC circuits are commonly used in electronics. AC circuits can be easily converted to different voltages using transformers, while DC circuits require a different power supply for each voltage needed.

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