  We studied the temperature and magnetic field dependence of vortex
dissipation and critical current in the mixed-state of unconventional
superconducting alloys Ba(Fe$_{1-x}$Co$_x$)$_2$As$_2$ ($0.044 \leq x \leq
0.100$) through current-voltage measurements. Our results reveal that all the
electric field $E$ vs current density $j$ curves in the Ohmic regime merge to
one point ($j_0,E_0$) and that there is a simple relationship between the
critical current density $j_c$ and flux-flow resistivity $\rho_{\rm ff}$:
$\rho_{\rm ff}/\rho_{\rm n} = (1- j_{c}/j_{0})^{-1}$, where $\rho_{\rm
n}=E_0/j_0$ is the normal-state resistivity just above the superconducting
transition. In addition, $E_0$ is positive for all five dopings, reflecting the
abnormal behavior of the flux-flow resistivity $\rho_{\rm ff}$: it increases
with decreasing magnetic field. In contrast, $E_0$ is negative for the
conventional superconductor Nb since, as expected, $\rho_{\rm ff}$ decreases
with decreasing magnetic field. Furthermore, in the under-doped and over-doped
single crystals of Ba(Fe$_{1-x}$Co$_x$)$_2$As$_2$, the parameter $E_0$ remains
temperature independent, while it decreases with increasing temperature for the
single crystals around optimal doping ($ 0.060\leq x\leq 0.072 $). This result
points to the co-existence of superconductivity with some other phase around
optimal doping.
