AC Parallel Circuit Formulas -

In this topic, we have listed some of the AC Parallel circuit formulas.

RL Parallel Circuit
RC Parallel Circuit
For RL Parallel and RC Parallel Circuit $I= \sqrt{I_{R}^{2}+I_{L}^{2}}$ $I= \sqrt{I_{R}^{2}+I_{C}^{2}}$	I= Total line current I_R= Current flow through the resistance I_L= Current flow through the inductance I_C= Current flow through the capacitance
For RL: $\frac{1}{Z}=\sqrt{\frac{1}{R^2}+\frac{1}{X_L^2}}$ For RC : $\frac{1}{Z}=\sqrt{\frac{1}{R^2}+\frac{1}{X_C^2}}$	Z= Impedance R= Resistance X_L= Inductive Reactance X_C= Capacitive Reactance
For RL: $\tan{\phi}=\frac{V_L}{V_R}\ =\frac{X_L}{R}$ For RC: $\tan{\phi}=\frac{V_C}{V_R}\ =\frac{X_C}{R}$	Circuit current I lags behind the applied voltage V by $\phi^{\circ }$

RLC Parallel Circuit
For RLC Parallel: $I= \sqrt{I_R^2 + (I_L - I_C)^2}$	I= Total line current I_R= Current flow through the resistance I_L= Current flow through the inductance I_C= Current flow through the capacitance
For RLC Parallel: $Y = \sqrt{G^2 + (B_L - B_C)^2}$ $= \sqrt{G^2 + B^2}$ Where, $Y = \frac{1}{Z}$ $G = \frac{1}{R}$ $B_L = \frac{1}{\omega L}$ $B_C = \omega C$	Y =Admittance G=Conductance B_L=Inductive Susceptance B_C= Capacitive Susceptance B= Net Susceptance= B_L– B_C
$\cos \phi = \frac{G}{Y}$ $\tan \phi = \frac{B}{G}$	Y =Admittance G=Conductance B= Net Susceptance= B_L– B_C
For RLC Parallel Resonance: $f_r = \frac{1}{2\pi\sqrt{LC}}$ $\omega_r = \frac{1}{\sqrt{LC}}$	f_r = Resonance frequency L= Inductance C= Capacitance