Figure below shows the circuit containing alternating voltage source V=V_{0}sinω connected to a resistor of resistance R
Let at any instant of time ,i is the current in the circuit ,then from Kirchhoff�s loop rule
V_{0}sinωtRi
or
i=(V_{0}/R)sinωt
=i_{0}sinωt ----(8)
Where, i_{0}=V_{0}/R ----(9)
From instantaneous values of alternating voltage and current ,we can conclude that in pure resistor ,the current is always in phase with applied voltage