AC Series Circuit Formulas

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 V_R= Voltage across resistance V_L= Voltage across inductance V_C= Voltage across capacitance R= Resistance X_L= Inductive Reactance X_C= Capacitive Reactance
For RL: $Z= \sqrt{R^{2}+X_{L}^{2}}$ For RC : $Z= \sqrt{R^{2}+X_{C}^{2}}$	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 $\phi^{\circ }$

$V = \sqrt{V_R^2 + (V_L - V_C)^2}$ $V = I\sqrt{R^2 + (X_L - X_C)^2}$ When X_L > X_C	V= rms value of the applied voltage I= rms value of the circuit current V_R= Voltage across resistance V_L= Voltage across inductance V_C= Voltage across capacitance R= Resistance X_L= Inductive Reactance X_C= Capacitive Reactance
$Z =\sqrt{R^2 + (X_L - X_C)^2}$ When X_L > X_C	Z= Impedance R= Resistance X_L= Inductive Reactance X_C= 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, X_L > X_C

$f_r = \frac{1}{2\pi\sqrt{LC}}$ $\omega_r = \frac{1}{\sqrt{LC}}$	f_r = 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 = $\frac{f_r}{Q}$	f_r = Resonance frequency Q-factor = Quality factor
$f_r =\sqrt{{f_1}{f_2}}$	f_r = Resonance frequency f ₂ = Upper cut-off frequency f ₁ = Lower cut-off frequency