A.C. cable theory and its implications on the measurements of the membrane electric parameters

The solution to the a.c. cable equations for a leaky non-inductive coaxial cable is presented. It is shown that the exact solution can be expressed in terms of a simple Ohm's law formulation modified by multiplicative factors. A numerical analysis of these factors shows that the formulation reduces to a simple Ohm's law for the case of infinite impedance terminations, if the voltage is recorded at a distance 0·421/λ from the centre of a midpoint current injection, 1 is the half-length of the cell and A the space constant. The same result applies to the case of external current injection if the voltage is recorded at a distance of 0·581/λ from the centre of the cell segment of length 21. This thus allows an easy and accurate computation of the membrane resistance and capacitance. It is also shown that the accuracy obtained in these computations can be estimated quantitatively. The actual values of the accuracy obtained in a.c. studies of Nitella translucens are presented.