Cable theory - calculating cable length using graphs

In summary, the task at hand is to determine cable length (lambda), area specific conductance (Gm), and internal resistivity of a cell using a simulation program. The program allows for the injection of a current and the distance of the electrode from the center of the cell to be changed, with the output being the membrane voltage. After tabulating and plotting the data, the next step is to find lambda and conductance, which can be done using a few methods such as graphing on semi-log paper or using the exponential voltage decay. Once lambda is known, the internal resistivity can be calculated.
  • #1
af86
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Homework Statement



Using a simulation program I must determine cable length (lambda), area specific conductance (Gm) and internal resistivity of a cell.

The program allows you to inject a current (in uA) and change the electrode distance from the centre of the cell.

The simulator then outputs a membrane voltage in mV.

Length is 60mm
Radius is 0.5mm

Homework Equations



J = V Gm

λ = [Gm (ro+ri) πd]-1/2

The Attempt at a Solution



I have tabulated an injected current of 1uA against the distance, keeping current at 1uA and increasing distance by 2mm. I then plotted the membrane voltage against the distance.

Unsure how to find lambda and conductance from this point.

please help!
 
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  • #2
Good grief. This is neuroscience. I'm sure you've generated a lot of head scratching from thos trying to understand what at first looks like a problem in electrical cables and voltaic cells.
 
  • #3
Phrak said:
Good grief. This is neuroscience. I'm sure you've generated a lot of head scratching from thos trying to understand what at first looks like a problem in electrical cables and voltaic cells.

Which of course it is based on.

To the OP, you might look http://en.wikipedia.org/wiki/Cable_theory" for some guidance. Is your model just outputting the steady state Em as a function of distance? If so, lambda can be obtained a few ways.

You could graph on semi-log paper or use the relation that the voltage decay is exponential--i.e.at one lambda,the delta V falls to 37% of the delta V at x=0. That delta V in the steady state is just i*Rm, or in terms of conductance, i/Gm is what you're calling Gm is the reciprocal of Rm. Once lambda is known,you should be able to work out the internal resistivity.
 
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1. How do I calculate the cable length using graphs?

To calculate the cable length using graphs, you need to first plot a graph of the cable's resistance versus distance. Then, measure the slope of the line on the graph, which represents the cable's resistance per unit length. Finally, divide the total resistance of the cable by the resistance per unit length to get the cable's length.

2. What is cable theory?

Cable theory is a mathematical model used to describe the electrical properties of long, thin structures such as nerve fibers or electrical cables. It takes into account factors such as the cable's length, diameter, and resistance to calculate its electrical behavior.

3. What are the assumptions made in cable theory?

The main assumptions made in cable theory are that the cable is long and uniform, has a constant cross-sectional area, and is made of a homogeneous material with a linear relationship between current and voltage. These assumptions allow for simplification of the mathematical calculations.

4. Can cable theory be applied to real-world situations?

Yes, cable theory is commonly used in various fields such as neuroscience, electrical engineering, and telecommunications to predict and analyze the behavior of cables in real-world scenarios. However, it is important to note that the model may not be accurate in certain complex situations.

5. Are there any limitations to using cable theory?

While cable theory is a useful tool for predicting the behavior of cables, it has its limitations. It does not take into account factors such as temperature, non-linear relationships between current and voltage, and the presence of other components or materials in the cable. These limitations may affect the accuracy of the results in certain situations.

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