Descriptions of AC electrical circuits

For DC circuit V/I = R

For AC circuits V/I = Z

Here Z is impedance.

# The R branch:
This is a simple ac circuit shown in figure from simple circuits.
For voltage

V = iR
Or, iR = Vm Sinwt

Or, i = Vm Sinwt / R

For current,

Im = Vm / R

Or, R = Vm / Im

Or, ZR = Vm / Im = R<0

For resistive branch v and i are in phase.

# Power: Ac power supplies

P = Vi
= Vm Sinwt X Im Sinwt
= 1/2 Vm Im (1-Cos2wt)
= 1/2 Vm Im – 1/2Vm Im Cos2wt