AC Circuits & EM Waves

Effective Study Strategies

• Understand AC vs DC: AC changes direction periodically (sinusoidal), DC is constant. Key parameters: frequency (f), angular frequency (ω = 2πf), time period (T = 1/f).
• Master RMS values: V_rms = V₀/√2 ≈ 0.707V₀. RMS is the effective DC equivalent value for power calculations.
• Differentiate circuit elements: Resistor (V and I in phase), Capacitor (I leads V by 90°), Inductor (V leads I by 90°).
• Learn impedance formulas: Z_R = R, Z_C = 1/(ωC), Z_L = ωL. For series: Z = √(R² + (X_L – X_C)²).
• Visualize phase relationships: Use phasor diagrams to represent phase differences between voltage and current.
• Understand power factor: cosθ = P/(V_rmsI_rms). For resistive: cosθ=1, capacitive/inductive: cosθ=0, RLC: 0
• Master resonance: Occurs when X_L = X_C ⇒ ω = 1/√(LC). Series: Z minimum, I maximum; Parallel: Z maximum, I minimum.
• Connect EM wave concepts: Transverse waves, perpendicular E and B fields, speed c = 3×10⁸ m/s, produced by accelerating charges.

Exam Preparation Tips

• Memorize key formulas on flashcards: V = V₀sin(ωt), I = I₀sin(ωt), V_rms = V₀/√2, Z = √(R² + (X_L – X_C)²), f_r = 1/(2π√(LC)).
• Practice impedance calculations: For RC: Z = √(R² + (1/ωC)²); RL: Z = √(R² + (ωL)²); RLC: Z = √(R² + (ωL – 1/ωC)²).
• Solve phase angle problems: θ = tan^-1((X_L – X_C)/R). Positive θ: inductive (V leads I), negative θ: capacitive (I leads V).
• Understand modulation types: AM (amplitude varies), FM (frequency varies), PM (phase varies).
• Practice unit conversions: Hz to rad/s (ω = 2πf), mH to H (1 mH = 0.001 H), µF to F (1 µF = 10^-6 F).
• Time yourself on complex problems: Set a timer for 3-4 minutes per problem to simulate exam conditions.

Common Pitfalls to Avoid

• Confusing peak, RMS, and average values (V_peak = √2 × V_rms, V_avg = 0.637 × V_peak)
• Forgetting that capacitors block DC but pass AC (X_C = 1/(2πfC) decreases with frequency)
• Mixing up inductive and capacitive reactance (X_L ∝ f, X_C ∝ 1/f)
• Assuming power dissipation occurs in pure L or C circuits (P = V_rmsI_rmscosθ, cos90°=0)
• Confusing series and parallel resonance properties (series: min Z, max I; parallel: max Z, min I)
• Forgetting that EM waves are transverse (E⊥B⊥direction of propagation)
• Mixing up AM and FM frequency ranges (AM: 540-1600 kHz, FM: 88-108 MHz)

Circuit Element Comparison