Figure below shows the circuit containing alternating voltage source V=V0sinω 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
V0sinωtRi
or
i=(V0/R)sinωt
=i0sinωt                                                ----(8)
Where, i0=V0/R Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â ----(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