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

$ℰ\mathrm{\&}ℳ$ (Vol. 2):Template:Spaces 5:Electric Charges and FieldsTemplate:Spaces 6:Gauss's LawTemplate:Spaces 7:Electric PotentialTemplate:Spaces 8:CapacitanceTemplate:Spaces 9:Current and ResistanceTemplate:Spaces 10:Direct-Current CircuitsTemplate:Spaces 11:Magnetic Forces and FieldsTemplate:Spaces 12:Sources of Magnetic FieldsTemplate:Spaces 13:Electromagnetic InductionTemplate:Spaces 14:InductanceTemplate:Spaces 15:Alternating-Current CircuitsTemplate:Spaces 16:Electromagnetic Waves

Chapter 15

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For quiz at QB/d_cp2.15

Template:Colbegin AC voltage and current $v=V_0\sin (\omega t-\varphi )$ if $i=I_0\sin \omega t.$
RMS values $I_{rms}=\frac{I_0}{\sqrt{2}}$ and $V_{rms}=\frac{V_0}{\sqrt{2}}$
Impedance $V_0=I_{0}X$
Resistor $V_0=I_0{X}_R,\varphi =0,$ where $X_R=R$
Capacitor $V_0=I_0{X}_C,\varphi =-\frac{\pi }{2},$ where $X_C=\frac{1}{\omega C}$
Inductor $V_0=I_0{X}_L,\varphi =+\frac{\pi }{2},$ where $X_L=\omega L$
RLC series circuit $V_0=I_{0}Z$ where $Z=\sqrt{R^2+{(X_L-X_C)}^2}$ and $\varphi ={\tan }^{-1}\frac{X_L-X_C}{R}$
Resonant angular frequency ${\omega }_0=\sqrt{\frac{1}{LC}}$
Quality factor $Q=\frac{{\omega }_0}{\mathrm{\Delta }\omega }=\frac{{\omega }_{0}L}{R}$
Average power $P_{ave}=\frac{1}{2}{I}_0{V}_0\cos \varphi =I_{rms}{V}_{rms}\cos \varphi$
Transformer voltages and currents $\frac{V_S}{V_P}=\frac{N_S}{N_P}=\frac{I_P}{I_S}$