AC Circuit Containing Resistance Only

Suppose an alternating sinusoidal voltage E = E0 ejωt is applied across a pure resistance R.

The current through the resistance at any instant t is,
        I = E/R = E₀e^jωt /R = I₀ ejωt

Here,         I₀ = E₀ /R.

Actual value of Current
        = Imaginary part of I₀ e_jωt = I₀ sin ωt.
. :        I = I₀ sin ωt
Hence the current is in phase with the driving voltage.