Figure below shows the circuit containing alternating voltage source V=V_{0}sinÏ‰ 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}sinÏ‰tRi
or
i=(V_{0}/R)sinÏ‰t
=i_{0}sinÏ‰t 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 ----(8)
Where, i_{0}=V_{0}/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