# AC circuit with a Resistor

In any circuit the ratio of the effective voltage to the effective current is defined at the impedance Z of the circuit. Its unit is ohm.
Phasors and phasor diagrams
In the study of A.C. circuits, we shall come across alternating voltage and currents which have the same frequency but differ in phase with each other.

It is found that the study of A.C. circuits becomes simple, if alternating currents and voltages are treated as rotating vectors or more correctly as ‘phasors’.
The phase angle between the two quantities is also represented in the vector diagram.
A diagram representing alternating voltage and current as vectors with the phase angle between them is known as phasor diagram.

##### AC circuit with a resistor :

Instantaneous current

$\displaystyle i=\frac{e}{R}$

$\displaystyle i=\frac{e_0 sin\omega t}{R}$

i = i0 sin ωt

where i0 = eo/R = current amplitude.  Thus the voltage and the current in an A.C. circuit containing pure resistance are is phase.