Class-12th Ch-7 (Alternating Current)

✍️ Class 12 Physics – Chapter 7: Alternating Current (AC)

Alternating Current (AC) is a type of electric current that changes its direction and magnitude periodically. Unlike Direct Current (DC), AC reverses direction in a sinusoidal form.

General equation for AC:

Where:

• I₀ = peak current

• ω = angular frequency = 2πf

• f = frequency

• t = time

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📌 RMS and Average Values

Since AC changes over time, we use effective values:

• RMS Current:
  I_rms = I₀ / √2

• RMS Voltage:
  V_rms = V₀ / √2

• Average current over full cycle = 0

• Average over half cycle:
  I_avg = (2 × I₀) / π

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🔌 AC Through Resistor, Inductor & Capacitor

1. Resistor (R):

• Voltage and current are in phase

• Power consumed:
  P = I_rms² × R

2. Inductor (L):

• Current lags voltage by 90°

• Inductive reactance:
  X_L = ωL

• No real power consumed

3. Capacitor (C):

• Current leads voltage by 90°

• Capacitive reactance:
  X_C = 1 / (ωC)

• No real power consumed

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⚡ LCR Series AC Circuit

• Total Impedance (Z):
  Z = √(R² + (X_L - X_C)²)

• Phase angle:
  tan(φ) = (X_L - X_C) / R

• Current:
  I = V₀ / Z

• Power factor:
  cos(φ) = R / Z

• Average power:
  P_avg = V_rms × I_rms × cos(φ)

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🎯 Resonance in LCR Circuit

Resonance occurs when:

• Resonant frequency:
  f₀ = 1 / (2π√(LC))

• Impedance is minimum: Z = R

• Current is maximum at resonance

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🔄 Transformers (Ideal)

Used to step-up or step-down AC voltage using mutual induction.

• Voltage ratio:
  V_s / V_p = N_s / N_p

• Current ratio:
  I_s / I_p = N_p / N_s

• Ideal power conservation:
  V_p × I_p = V_s × I_s

Where:

• V_p, V_s = primary & secondary voltage

• I_p, I_s = primary & secondary current

• N_p, N_s = turns in primary & secondary coil

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📚 Important Derivations

• RMS value of AC

• Impedance of LCR circuit

• Resonance condition

• Transformer equations

• Average power in AC circuit

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✅ Why It Matters

This chapter is highly important for:

• CBSE Class 12 Board Exams

• JEE & NEET Physics

• Future concepts in electronics and electrical engineering