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 |