gen-define-phasor-analysis-and-give-one-short-worked-example-04ea

Define phasor analysis and give one short worked example.

# Phasor Analysis **Phasor analysis** is a technique for analyzing AC circuits operating at steady-state sinusoidal conditions. It transforms time-domain differential equations into algebraic equations by representing sinusoidal voltages and currents as complex numbers (phasors). ## Key Concepts: - A sinusoidal signal **v(t) = V_m cos(ωt + φ)** is represented as a phasor **V = V_m∠φ** (or V_m e^(jφ)) - Time derivatives become multiplications by jω - Circuit analysis uses complex impedances instead of R, L, C --- ## Worked Example **Problem:** Find the current through a series RL circuit where R = 4Ω, L = 3mH, driven by v(t) = 10cos(1000t) V. **Solution:** 1. **Convert to phasor domain:** - V = 10∠0° V (using cosine as reference) - ω = 1000 rad/s 2. **Calculate impedance:** - Z_R = R = 4Ω - Z_L = jωL = j(1000)(0.003) = j3Ω - Z_total = 4 + j3 = 5∠36.87° Ω 3. **Find phasor current:** - I = V/Z = (10∠0°)/(5∠36.87°) = 2∠-36.87° A 4. **Convert back to time domain:** - **i(t) = 2cos(1000t - 36.87°) A** The current lags the voltage by 36.87° due to the inductor.