NEB Class 12 Physics Alternating Currents Notes in PDF Complete Handwritten. Physics Notes 2081: All Chapters | New Curriculum | Class 12 Physics Notes download.
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NEB Class 12 Physics Alternating Currents Note Handwritten in PDF
Peak Value and RMS Value
AC voltage and current vary sinusoidally:
- v = V₀ sinωt, i = I₀ sinωt
RMS (Root Mean Square) values:
- V_rms = V₀/√2 ≈ 0.707 V₀
- I_rms = I₀/√2 ≈ 0.707 I₀
Why RMS is important:
- RMS value is the equivalent DC that produces the same heating (power dissipation)
- All AC ratings (230V, 50Hz supply in Nepal) are RMS values
- Peak voltage = 230√2 ≈ 325 V (this is why capacitors must be rated > 325V)
AC Through a Resistor
- V = V₀ sinωt, I = I₀ sinωt where I₀ = V₀/R
- V and I are in phase (φ = 0)
- Power: P = V_rms × I_rms = I²_rms × R (real power, non-zero)
AC Through an Inductor
- V = V₀ sinωt, I = I₀ sin(ωt − π/2)
- Current lags voltage by 90°
- Inductive reactance: X_L = ωL (opposition to AC by inductor)
- Higher frequency → higher X_L → inductor blocks high-frequency signals
- Power: P = V_rms × I_rms × cos90° = 0 (no power consumed)
AC Through a Capacitor
- V = V₀ sinωt, I = I₀ sin(ωt + π/2)
- Current leads voltage by 90°
- Capacitive reactance: X_C = 1/ωC (opposition to AC by capacitor)
- Higher frequency → lower X_C → capacitor passes high-frequency signals (blocks DC)
- Power: P = 0 (no power consumed)
Series LCR Circuit
Impedance: Z = √(R² + (X_L − X_C)²)
Phase angle: tanφ = (X_L − X_C)/R
Current amplitude: I₀ = V₀/Z
Phasor diagram:
- V_R along I (in phase with current)
- V_L leads I by 90° (upward)
- V_C lags I by 90° (downward)
- V_L and V_C partially cancel
- Net reactive component = |X_L − X_C|
Series Resonance
Condition: X_L = X_C → ωL = 1/ωC
Resonant frequency: f₀ = 1/(2π√LC)
At resonance:
- Z = R (minimum impedance → maximum current)
- φ = 0 (power factor = 1, purely resistive)
- V_L = V_C but they cancel → whole supply appears across R
Quality factor Q: Q = ω₀L/R = 1/(ω₀CR) = (1/R)√(L/C)
- High Q → sharp resonance (narrow bandwidth) → selective circuit
- Voltage magnification at resonance: V_L or V_C = Q × V_supply
- Radio tuning: adjust C to change resonant frequency to match desired radio station
Power in AC Circuits
True (real) power: P = V_rms × I_rms × cosφ
Power factor: cosφ = R/Z
- Pure resistor: cosφ = 1, P = V_rms × I_rms (maximum power)
- Pure inductor/capacitor: cosφ = 0, P = 0 (wattless current)
- LCR circuit: 0 ≤ cosφ ≤ 1
Wattless current: The component of current that is 90° out of phase with voltage it flows back and forth but does no net work. Reactive loads (motors, fluorescent lights) have large wattless currents power companies charge for apparent power (VA) not just real power (W), which is why power factor correction is important in industry.
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Frequently Asked Questions
What is RMS value of AC and why is it used?
RMS value is the equivalent DC that produces same heating effect as the AC. V_rms = V₀/√2 ≈ 0.707V₀. Nepal’s household supply is 230V rms at 50 Hz meaning peak voltage is 230×√2 ≈ 325V. RMS values are used because power calculations P = I²R require mean of I², which equals I²_rms.
What is inductive reactance and capacitive reactance Class 12?
Inductive reactance X_L = ωL increases with frequency inductor blocks high-frequency signals. Capacitive reactance X_C = 1/ωC decreases with frequency capacitor passes high-frequency and blocks DC. In inductor, current lags voltage by 90°. In capacitor, current leads voltage by 90°. Both consume zero average power.
What is the condition for series resonance in LCR circuit?
Series resonance: X_L = X_C, so ωL = 1/ωC. Resonant frequency f₀ = 1/(2π√LC). At resonance: impedance Z = R (minimum), current I = V/R (maximum), power factor = 1 (purely resistive), and V_L = V_C (they cancel). Used in radio tuning adjust C to match resonant frequency of desired station.
What is quality factor Q in AC circuits Class 12?
Quality factor Q = ω₀L/R = 1/(ω₀CR) = (1/R)√(L/C). High Q means sharp resonance with narrow bandwidth better frequency selectivity. Voltage across L or C at resonance = Q × supply voltage (voltage magnification). High Q circuits are used in radio receivers, oscillators, and filters requiring sharp frequency discrimination.
What is power factor in AC circuits Class 12?
Power factor cosφ = R/Z = true power/apparent power. For pure resistor cosφ = 1 all power consumed. For pure inductor or capacitor cosφ = 0 no power consumed (wattless current). For LCR circuit: 0 ≤ cosφ ≤ 1. Low power factor wastes energy in transmission lines industries must maintain high power factor.
What is impedance of LCR series circuit Class 12?
Impedance Z = √(R² + (X_L−X_C)²). Total opposition to AC in a series LCR circuit. Phase angle tanφ = (X_L−X_C)/R. Current I = V/Z. When X_L > X_C circuit is inductive (current lags). When X_C > X_L circuit is capacitive (current leads). At resonance X_L = X_C and Z = R (minimum impedance).
What is phasor diagram in AC circuits Class 12?
Phasor diagram represents AC quantities as rotating vectors. V_R is along current I (in phase). V_L is 90° ahead of I (leads). V_C is 90° behind I (lags). Net voltage V = √(V_R² + (V_L−V_C)²). Phase angle φ between V and I is found from tanφ = (V_L−V_C)/V_R. Phasors simplify complex AC calculations significantly.
Which AC circuits topics are most important for Exam?
Most important: RMS values derivation (2 marks), series resonance condition and frequency (4 marks), impedance formula with numericals (4 marks), quality factor (2 marks), power factor (2 marks), and phasor diagrams (2 marks). Series LCR resonance numericals appear in almost every NEB Class 12 board examination paper.