EMI & AC — Alternating Current Circuits (Medium)

Quick Recap — Alternating Current Circuits

• AC values: $I=I_0\sin\omega t$; $I_{rms}=\dfrac{I_0}{\sqrt2}$, $V_{rms}=\dfrac{V_0}{\sqrt2}$.
• Reactances: inductive $X_L=\omega L$ (grows with $f$); capacitive $X_C=\dfrac{1}{\omega C}$ (falls with $f$).
• Series LCR: impedance $Z=\sqrt{R^2+(X_L-X_C)^2}$; resonance at $\omega_0=\dfrac{1}{\sqrt{LC}}$, where $X_L=X_C$, $Z=R$ (minimum), and current is maximum.
• Power: $P=V_{rms}I_{rms}\cos\phi$, power factor $\cos\phi=\dfrac{R}{Z}$. A pure inductor or capacitor consumes no average power (wattless current).
• Ideal transformer: $\dfrac{V_s}{V_p}=\dfrac{N_s}{N_p}=\dfrac{I_p}{I_s}$ (power conserved).

Worked mini-example. A series circuit has $R=30\ \Omega$, $X_L=80\ \Omega$, $X_C=40\ \Omega$: $Z=\sqrt{30^2+(80-40)^2}=\sqrt{900+1600}=50\ \Omega$, and $\cos\phi=\dfrac{30}{50}=0.6$.