The RMS sum of the current and voltage quantities as a phase varies for the vector that presents the maximum or peak values, separating the peak amounts of the time terms above √2 to the main current-voltage phase equation. The RMS relation is projected as.
I=\\frac { { I }_{ m } }{ \\sqrt { 2 } } <\ hetaI=2 Im<θ
V=\\frac { R.{ I }_{ M } }{ \\sqrt { 2 } } <\ hetaV=2 R.Im<θ
R=\\frac {V }{ I } =\\frac { (R.{ I }_{m })/\\sqrt { 2 } <\ heta }{ { (I }_{m })/\\sqrt { 2 } <\ heta }R=IV=(Im)/2<θ (R.Im)/2<θ
And the phase relationship can be obtained as follows:
V=R.{ I }_{rms }<\ heta V=R.irms<θ
I={ I }_{ rms }<\ hetaI=Irms<θ
V<{ \ heta }_{ V }={ I }<{ \ heta }_{ I } V<θ V=I<θ I
{ \ heta }_{ v }={ \ heta }_{ i }(in-phase)θ v=θ i(in−phase)
It presents that a fixed resistance in an AC system produces an equation between its current and voltage phasors in the same way as it operates in a DC system with the same resistor current and voltage diagram. However, in the DC diagram, this equation is usually named resistance, as introduced by Ohm's law.