132
A.5 Derivation of the input impedance of a one-dimensional cable
Using the relationship for the steady-state voltage distribution for a one-dimensional cable:
/ ы ∖
υ(rr) = υ0exp I--—I (A.l)
∖ ^id /
The current into the point source (the originating cell) must be equal to the sum of all of
the currents that flow through the membranes of all cells in the network, and the current
through the membranes is the the cell voltage divided by the membrane resistance so:
(A.2)
Substituting A.l into A.2 yields:
. 2woAιr>
l0 = ~~R---
. ʃɪm
Rearranging terms, keeping in mind that RiniD = ^o∕⅛
(A.3)
mlD 2λ
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