For RL and RC Series Circuit:
| For RL Series Circuit \(V= \sqrt{V_{R}^{2}+V_{L}^{2}}\) \(V=I \sqrt{R^{2}+X_{L}^{2}}\) For RC Series Circuit \(V= \sqrt{V_{R}^{2}+V_{C}^{2}}\) \(V=I \sqrt{R^{2}+X_{C}^{2}}\) | V= rms value of the applied voltage I= rms value of the circuit current VR= Voltage across resistance VL= Voltage across inductance VC= Voltage across capacitance R= Resistance XL= Inductive Reactance XC= Capacitive Reactance |
| For RL: \(Z= \sqrt{R^{2}+X_{L}^{2}}\) For RC : \(Z= \sqrt{R^{2}+X_{C}^{2}}\) | 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 RLC Series Circuit:
| \(V = \sqrt{V_R^2 + (V_L – V_C)^2}\) \(V = I\sqrt{R^2 + (X_L – X_C)^2}\) When XL > XC | V= rms value of the applied voltage I= rms value of the circuit current VR= Voltage across resistance VL= Voltage across inductance VC= Voltage across capacitance R= Resistance XL= Inductive Reactance XC= Capacitive Reactance |
| \(Z =\sqrt{R^2 + (X_L – X_C)^2}\) When XL > XC | Z= Impedance R= Resistance XL= Inductive Reactance XC= Capacitive Reactance |
| \(\cos \phi = \frac{R}{Z}\) | \(\cos \phi\) = Power Factor Z= Impedance R= Resistance |
| \(\tan \phi = \frac{V_L – V_C}{V_R} = \frac{X_L – X_C}{R}\) | \(\phi\) = Angle between supplied voltage and circuit current, Here, XL > XC |
For Series Resonance:
| \(f_r = \frac{1}{2\pi\sqrt{LC}}\) \(\omega_r = \frac{1}{\sqrt{LC}}\) | fr = Resonance frequency L= Inductance C= Capacitance |
| Q-factor = \( \frac{V_L}{V}=\frac{V_C}{V}=\frac{X_L}{R}=\frac{X_C}{R}\) Q-factor = \( \frac{1}{R}\sqrt{\frac{L}{C}}\) | Q-factor = Quality factor L= Inductance C= Capacitance R= Resistsnce |
| Bandwidth = f 2 − f 1 | f 2 = Upper cut-off frequency f 1 = Lower cut-off frequency |
| Bandwidth = \(\frac{f_r}{Q}\) | fr = Resonance frequency Q-factor = Quality factor |
| \(f_r =\sqrt{{f_1}{f_2}}\) | fr = Resonance frequency f 2 = Upper cut-off frequency f 1 = Lower cut-off frequency |