Class 12 Physics Formula Sheet

1. Basic AC Equations & RMS Values

• AC Voltage & Current: e = e₀ sin(ωt) (Where e₀ = peak voltage, ω = angular frequency = 2πf) and I = I₀ sin(ωt ± φ)
• Root Mean Square (RMS) / Virtual Value: I_rms = I₀ / √2 ≈ 0.707 I₀ (Similarly, E_rms = E₀ / √2 ≈ 0.707 E₀)
• Mean / Average Value (over a full cycle): I_avg = 0 (Over a half cycle: I_avg = 2I₀ / π ≈ 0.637 I₀)

2. AC Circuits with Pure Components

• Pure Resistor (R): Voltage and current are in phase (φ = 0). X_R = 0, Z = R.
• Pure Inductor (L): Current lags voltage by 90° (π/2).
  Inductive Reactance (X_L): X_L = ωL = 2πfL (Unit: Ohm [Ω])
• Pure Capacitor (C): Current leads voltage by 90° (π/2).
  Capacitive Reactance (X_C): X_C = 1 / (ωC) = 1 / (2πfC) (Unit: Ohm [Ω])

3. Series LCR Circuit & Resonance

• Impedance (Z): Z = √[R² + (X_L - X_C)²] (Peak current I₀ = E₀ / Z)
• Phase Angle (φ): tan(φ) = (X_L - X_C) / R
• Series Resonance Condition: X_L = X_C → ωL = 1 / (ωC)
  Resonant Frequency (f_r): f_r = 1 / [2π √(LC)] (At resonance: Z = R [minimum], Current is maximum, cos(φ) = 1)
• Quality Factor (Q-factor): Q = (ω_r L) / R = 1 / (R √(C/L))

4. Power in AC Circuits & Wattless Current

• Average Power (P_avg): P_avg = E_rms × I_rms × cos(φ) (Where cos(φ) = R / Z is the Power Factor)
• Wattless Current: The component of current I_rms sin(φ) that consumes zero net power in a pure inductor or capacitor circuit.

5. Electrical Machines (Transformer & AC Generator)

• Transformer Principle (Mutual Induction):
  • Voltage & Turns Ratio: E_s / E_p = N_s / N_p = k (k = transformation ratio)
  • Current Ratio (for ideal transformer): E_pI_p = E_sI_s → I_s / I_p = N_p / N_s
  • Efficiency (η): η = (Output Power / Input Power) × 100% = (E_sI_s / E_pI_p) × 100%
• Step-up vs Step-down:
  • Step-up: N_s > N_p, E_s > E_p, k > 1
  • Step-down: N_s < N_p, E_s < E_p, k < 1