Basic Electrical Engineering

Sinusoids, RMS, and phasors

Reactance and impedance

Combining impedances and Ohm's law for AC

The series RLC circuit

Complex power and the power triangle

Power factor correction

Series resonance

Exam strategy

Key equations

Worked examples

Common pitfalls

• •Mixing $f$ and $\omega$: reactance uses $\omega=2\pi f$, not $f$. Plugging $60$ instead of $377$ into $X_L=\omega L$ understates the reactance by a factor of $2\pi$.
• •Capacitor reactance sign: $X_C$ contributes $-j/(\omega C)$ to impedance. Forgetting the minus makes the circuit look inductive and flips the power factor from leading to lagging.
• •Lead/lag confusion: lagging power factor means the current lags the voltage (inductive, $+Q$). 'Leading' is capacitive. Reversing them gives the wrong sign of reactive power.
• •Using peak instead of RMS for power: $P=V_{\text{rms}}I_{\text{rms}}\cos\theta$ needs RMS values. Using $V_{\max}$
• •Real power in reactance: $P=I^2R$ uses only the resistance. Reactive elements store and return energy — they dissipate no average power, so never put $X$ into the $P$ formula.
• •Conjugate in complex power: $\mathbf{S}=\mathbf{V}\mathbf{I}^{*}$ uses the conjugate of the current. Using $\mathbf{V}\mathbf{I}$ flips the sign of $Q$ and mislabels inductive vs capacitive.
• •Resonance reactances aren't zero: at resonance $X_L=X_C$ individually can be large; only their difference cancels. The L and C voltages can exceed the source voltage by the factor $Q$.

References

• NCEES FE Reference Handbook — Electrical and Computer Engineering (AC Circuits, Impedance)
• NCEES FE Reference Handbook — Electrical and Computer Engineering (AC Power, Complex Power)
• NCEES FE Reference Handbook — Electrical and Computer Engineering (Resonance)