** Next:** Finite cable
** Up:** Steady state and boundary
** Previous:** Steady state and boundary

In this case, we assume that at
*x*=0 the voltage is clamped to *V*=*V*_{0}. The boundedness of the
voltage as means that we must take
| |
(13) |

It is now clear why is called a *space-constant*, it
determines the voltage attenuation with distance.
Alternatively, we could demand that the current at *x*=0 be specified
as *I*_{0}. From (14) we see that

and since we get
The input resistance is the ratio of *V*(0)/*I*_{0} is thus
| |
(14) |

The input conductance for the semi-infinite cable is thus
**Note:** It is often convenient to introduce the dimensionless
space variable, and the *electrotonic length* of the
cable, This gets rid of all the divisions by in the exponentials and hyperbolic functions.

*G. Bard Ermentrout*

*1/10/1998*