Time and Space Constants
PSP's decay with time and with distance. This decay is largely dependent on resistance-capacitance
characteristics of the membrane and can be characterized by the rate at which this decay occurs, as shown
below.
Time constant
VT = Vmax (1-e -T/) where VT= V at time T, and
=time constant of circuit.
when T = , (T = one time constant)
V = Vmax(1-e-1)
V = Vmax(0.63)
So, one time constant is the time it takes for the psp to reach 63% of its maximum value. As one moves away
from the current source (synapse) the total membrane capacitance increases so the the time to reach peak
increases. The larger the time constant of the membrane, more slowly the membrane reaches its peak
potential, all else being equal.
Space constant (also called length constant or characteristic length)
VX = VX=0 (e -x/)
where X = distance from source (synapse)
 = (Rm/Ri)1/2
at a distance of one space constant, X = 
thus, VX = Vx = 0 (e-1)
Vx = Vx=0(0.37)
So, at a distance of one space constant, the PSP has decayed to 37% of its value at the synapse. Or, to put it
another way, one space constant is the distance it takes for the PSP to decay to 37% of its initial value. The
larger the space constant, the more slowly the PSP decays with distance from the synapse. Note also that as
Rm increases, the space constant increases; as Ri decreases, the space constant increases.