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AC Parallel Circuit Formulas

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

For RL and RC Parallel Circuit:

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
IR= Current flow through the resistance
IL= Current flow through the inductance
IC= 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
XL= Inductive Reactance
XC= 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 }

For parallel RLC Circuit:

RLC Parallel Circuit
For RLC Parallel:
I= \sqrt{I_R^2 + (I_L - I_C)^2}		I= Total line current
IR= Current flow through the resistance
IL= Current flow through the inductance
IC= 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
BL=Inductive Susceptance
BC= Capacitive Susceptance
B= Net Susceptance= BL– BC
\cos \phi = \frac{G}{Y}
\tan \phi = \frac{B}{G}		Y =Admittance
G=Conductance
B= Net Susceptance= BL– BC
For RLC Parallel Resonance:
f_r = \frac{1}{2\pi\sqrt{LC}}

\omega_r = \frac{1}{\sqrt{LC}}		fr = Resonance frequency
L= Inductance
C= Capacitance
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