Key Equations

Key Equations

AC voltage	$v=V_0\text{sin}\omega t$
AC current	$i=I_0\text{sin}\omega t$
capacitive reactance	$\frac{V_0}{I_0}=\frac{1}{\omega C}=X_C$
rms voltage	$V_{\text{rms}}=\frac{V_0}{\sqrt{2}}$
rms current	$I_{\text{rms}}=\frac{I_0}{\sqrt{2}}$
inductive reactance	$\frac{V_0}{I_0}=\omega L=X_L$
Phase angle of an RLC series circuit	$\varphi ={\text{tan}}^{\mathrm{-1}}\frac{X_L-X_C}{R}$
AC version of Ohm’s law	$I_0=\frac{V_0}{Z}$
Impedance of an RLC series circuit	$Z=\sqrt{R^2+{\left(X_L-X_C\right)}^2}$
Average power associated with a circuit element	$P_{\text{ave}}=\frac{1}{2}{I}_0{V}_0\text{cos}\varphi$
Average power dissipated by a resistor	$P_{\text{ave}}=\frac{1}{2}{I}_0{V}_0=I_{\text{rms}}{V}_{\text{rms}}=I_{\text{rms}}^{2}R$
Resonant angular frequency of a circuit	${\omega }_0=\sqrt{\frac{1}{LC}}$
Quality factor of a circuit	$Q=\frac{{\omega }_0}{\text{Δ}\omega }$
Quality factor of a circuit in terms of the circuit parameters	$Q=\frac{{\omega }_{0}L}{R}$
Transformer equation with voltage	$\frac{V_{\text{S}}}{V_{\text{P}}}=\frac{N_{\text{S}}}{N_{\text{P}}}$
Transformer equation with current	$I_{\text{S}}=\frac{N_{\text{P}}}{N_{\text{S}}}{I}_{\text{P}}$