OpenStax University Physics/E&M/Alternating-Current Circuits

For quiz at QB/d_cp2.15
AC voltage and current $$v=V_0\sin(\omega t-\phi)$$ if $$i=I_0\sin\omega t.$$ RMS values $$I_{rms}=\tfrac{I_0}{\sqrt 2}$$ and $$V_{rms}=\tfrac{V_0}{\sqrt 2}$$ Impedance $$V_0=I_0X$$ Resistor $$V_0=I_0X_R,\;\phi=0,$$ where $$X_R=R$$ Capacitor $$V_0=I_0X_C,\;\phi=-\tfrac\pi 2,$$ where $$X_C=\tfrac 1{\omega C}$$ Inductor $$V_0=I_0X_L,\;\phi=+\tfrac\pi 2,$$ where $$X_L=\omega L$$ RLC series circuit $$V_0=I_0 Z$$ where $$ Z=\sqrt{R^2 + \left(X_L-X_C\right)^2}$$ and $$\phi=\tan^{-1}\frac{X_L-X_C}{R}$$ Resonant angular frequency $$\omega_0=\sqrt\tfrac{1}{LC}$$ Quality factor $$Q=\tfrac{\omega_0}{\Delta\omega}=\tfrac{\omega_0L}{R}$$ Average power $$P_{ave}=\frac 1 2 I_0V_0\cos\phi=I_{rms}V_{rms}\cos\phi$$ Transformer voltages and currents $$\tfrac{V_S}{V_P}=\tfrac{N_S}{N_P}=\tfrac{I_P}{I_S}$$