We have studied the nonlinear current-voltage characteristic of a two dimensional lattice Coulomb gas by Monte Carlo simulation. We present three different determinations of the power-law exponent $a(T)$ of the nonlinear current-voltage characteristic, $V

measureonlythelinearresistance,andnotEasfunctionofj,adi erentapproachisto

usetheNyquistformula[16],

whichrelates

the

linear

resistancetotheequilibriumvoltage

uctuations:

R=1

2T

GiventheJosephsonrelationweseeimmediatelythattheKuboformulaequalstheNyquist

relation.

Thelinearresistancehasbeensuccessfullyusedinasimulation[12]tolocatethe

Kosterlitz-ThoulesstransitiontemperatureTcofthe2DlatticeCoulombgas.They nd

the nitesizescalingrelationatTc:

L2R1+ ∞ ∞dt Iv(t)Iv(0) canbeused.1

dt～τ 1,where φisthegradientofthephaseoftheGinsburg-Landau

orderparameter[18].Therefore,weexpectthelinearresistance,Eq.(5),toscalelike

R～ξ 2atTc.AtTcthecorrelationlengthdivergesandiscutofbythe nitesizeLofthe

latticeandhenceRL2=constatTc,tolowestorder.Thescalingrelationhasalogarithmic

correctionwhichhasbeenincludedinEq.(6).Thiscorrectionisreadilyobtainedfromthe

correspondingcorrectiontermsfor1/ andλ[19].