ENEL220 PART ONE

Why do we use phasor analysis?

To replace differential equations with complex algebra in sinusoidal steady-state circuits.

In x(t) = A cos(ωt + φ), what do A, ω and φ represent?

Peak amplitude, angular frequency (rad/s), and phase angle.

How are frequency f and angular frequency ω related?

ω = 2πf, so f = ω/(2π).

How do you write V cos(ωt + φ) as a peak-value phasor?

V∠φ; the common time dependence is omitted, but ω is still needed for impedance.

What is Euler's equation?

e^(jθ) = cos θ + j sin θ.

What do positive and negative phase angles indicate?

Relative to a zero-phase cosine: positive leads; negative lags.

How are current and voltage phased for ideal R, L and C?

R: in phase. L: current lags by 90°. C: current leads by 90°.

What is impedance?

Z = Ṽ/Ĩ: complex opposition to AC, including phase; measured in ohms (Ω).

What are the impedances of R, L and C?

Z_R = R; Z_L = jωL; Z_C = 1/(jωC).

How do you find current from voltage and impedance phasors?

Ĩ = Ṽ/Z. In polar form, divide magnitudes and subtract phase angles.

How does increasing frequency affect L and C impedance magnitudes?

Inductor: increases (ωL). Capacitor: decreases (1/ωC).

How do ideal inductors and capacitors behave at DC steady state?

Inductor: short circuit. Capacitor: open circuit.

How do you combine impedances in series and parallel?

Series: Z_total = ΣZ. Parallel: 1/Z_total = Σ(1/Z).

What does positive or negative imaginary impedance indicate?

+jX: inductive, current lags voltage. −jX: capacitive, current leads voltage.

What is admittance, and when is it useful?

Y = 1/Z, measured in siemens (S); add admittances for parallel branches.