RLC parallel circuit formula and Phasor diagram

RLC in parallel

RCL parallel circuit can be considered as two reactance's XC and XL where the currents are in phase opposition in parallel with the resistor.

Through the use of  the phasor diagram the effective total resistance can be found  . It can be observed that IR is at the base of the right triangle and IL minus IC minus IL forming the perpendicular.

The amplitude of the resultant current is the hypotenuse.

To calculate the resultant we use the Pythagorean theorem . Ic and IL  are 180 degree out of phase  therefore cancel out. The resultant current is the difference between the two.

              

Impedance  phase angle  is calculated from the difference between IL and IC divided by IR