⚡ Quick Revision
Complete AC in one page
🎯 How to Use This Page
24 hours before exam: Go through entire page slowly
1 hour before exam: Read formula dump + common mistakes
5 minutes before exam: Flashcards only
One-Page Summary
1. AC Basics
V = V₀ sin(ωt) | I = I₀ sin(ωt + φ)
- ω = 2πf (angular frequency)
- V_rms = V₀/√2 = 0.707V₀ (RMS voltage)
- I_avg = 2I₀/π = 0.637I₀ (average over half cycle)
- Household "220V" means V_rms
2. Reactance
X_L = ωL = 2πfL | X_C = 1/(ωC) = 1/(2πfC)
- X_L ∝ f (inductor blocks high frequency)
- X_C ∝ 1/f (capacitor blocks DC)
- Both have dimension of resistance (Ω)
3. Phase Relationships (CIVIL)
- Resistor: V and I in phase (φ = 0)
- Inductor: V leads I by 90° (φ = +90°)
- Capacitor: I leads V by 90° (φ = -90°)
Memory: CIVIL → In C, I before V | In (V)L, V before I
4. LCR Circuit
Z = √[R² + (X_L - X_C)²]
I = V/Z | tan φ = (X_L - X_C)/R | cos φ = R/Z
- If X_L > X_C: Inductive (current lags)
- If X_C > X_L: Capacitive (current leads)
- If X_L = X_C: Resonance (in phase)
5. Resonance (Most Important!)
ω₀ = 1/√(LC) | f₀ = 1/(2π√(LC))
At resonance:
- Z = R (minimum)
- I = V/R (maximum)
- φ = 0 (in phase)
- cos φ = 1 (power factor maximum)
- V_L = V_C (can be >> V)
Q = ω₀L/R = (1/R)√(L/C) = V_L/V
Quality factor (voltage magnification)
6. Power
P = V_rms I_rms cos φ = I_rms² R
- ALWAYS use RMS values
- Never forget cos φ!
- Pure R: P = V²/R (cos φ = 1)
- Pure L or C: P = 0 (cos φ = 0, wattless)
7. Transformer
V_s/V_p = N_s/N_p | I_s/I_p = N_p/N_s | V_s I_s = V_p I_p
- Works only on AC (needs changing flux)
- Step-up: N_s > N_p → V_s > V_p, I_s < I_p
- Step-down: N_s < N_p → V_s < V_p, I_s > I_p
Formula Dump (Print This!)
V_rms = V₀/√2
I_rms = I₀/√2
I_avg = 2I₀/π
X_L = 2πfL
X_C = 1/(2πfC)
Z = √[R² + (X_L - X_C)²]
I = V/Z
tan φ = (X_L - X_C)/R
cos φ = R/Z
f₀ = 1/(2π√(LC))
P = V_rms I_rms cos φ
Q = ω₀L/R = (1/R)√(L/C)
Interactive Flashcards
Click to start flashcards
Use keyboard arrows or buttons below
Card 1 / 15
Memory Tricks
CIVIL
Capacitor: I before V
Inductor (VIL): V before I
Frequency Behavior
L is Lazy: Blocks high frequency
C is Choosy: Blocks DC (f=0)
Resonance
At resonance:
Z Minimum
I Maximum
cos φ = 1
Conversions
√2 ≈ 1.414
1/√2 ≈ 0.707
2/π ≈ 0.637
π ≈ 3.14
Common Mistakes Checklist
❌ Check These Before Submitting
| # | Mistake | Correct Approach |
|---|---|---|
| 1 | Using V₀ in power formula | ALWAYS use V_rms (or convert first) |
| 2 | Z = R + X_L + X_C | Z = √[R² + (X_L - X_C)²] |
| 3 | Forgetting cos φ in power | P = VI cos φ (not just VI) |
| 4 | Phase: "Current leads" means larger | Leads means reaches peak EARLIER |
| 5 | At resonance: V_L = V_C = 0 | V_L = V_C but NOT zero! |
| 6 | Peak-to-peak = V₀ | Peak-to-peak = 2V₀ |
| 7 | Not checking units | Always write unit in final answer |
| 8 | "220V" means V₀ = 220V | 220V is V_rms, V₀ = 311V |
Quick Facts to Remember
- ✓ AC instruments (voltmeter, ammeter) read RMS values
- ✓ Oscilloscope displays peak values
- ✓ Wattmeter reads average power (already includes cos φ)
- ✓ At DC (f=0): X_L = 0, X_C = ∞
- ✓ At very high f: X_L → ∞, X_C → 0
- ✓ Power factor: Always between 0 and 1
- ✓ Transformer works only on AC
- ✓ In series circuit: Current is same, voltages add as phasors
- ✓ Impedance dimension = Resistance dimension = [ML²T⁻³A⁻²]
- ✓ Resonance: X_L = X_C (not X_L + X_C = 0)
🎯 Final Pre-Exam Checklist
Day before exam:
- ☐ Wrote all formulas from memory
- ☐ Solved 5 mixed problems
- ☐ Reviewed common mistakes
- ☐ Can draw phasor diagrams quickly
- ☐ Know CIVIL by heart
Morning of exam:
- ☐ Quick formula revision (15 min)
- ☐ Read one-page summary (10 min)
- ☐ Solve 2 quick problems as warm-up
5 minutes before exam:
- ☐ Flashcards quick flip
- ☐ Deep breath
- ☐ Confidence: You've got this!
You're Ready! 🚀
You've mastered AC from basics to advanced.
Trust your preparation. Apply your knowledge.
Go ace that exam!