An alternating e.m.f. is supplied to a pure resistance investigate the phase relationship between current flowing through it and the applied e.m.f.

Explanation

Let R is a pure ohmic resistance (having no inductance) which is connected to source of alternating emf .
Let E = Instantaneous value of alternating emf
and E = `E_0sinomegat`
Let I = Current flowing in the circuit at any time t.
Instantaņeous emf due to source = Instantaneous value of potential drop across R.
E = IR
`I=E/R`
`I=E_0/Rsin omegat ` [Using eq.(i)]

But `E_0/R=I_0` = Peak value of alternating current in the circuit .
So `I=I_0 sin omegat " "...(ii)`
From eqns. (i) and (ii), it is clear that alternating emf is in same phase with alternating current. It is shown by the Fig. given below: