Questions
3–5 questions per paper
Difficulty
Medium-Hard
Importance
Core — never skip
Overview
Alternating Current (AC) describes the behavior of circuits where voltage and current vary sinusoidally over time. It is a cornerstone of Class 12 physics, bridging the gap between steady-state DC circuits and complex electromagnetic oscillations. Mastery of phasor diagrams and impedance is essential to solving both conceptual and numerical problems.
AC Circuits and Phasors
This sub-topic covers the behavior of R, L, and C components when subjected to a sinusoidal voltage source. The phase relationship between voltage and current is unique for each component, making phasor diagrams a critical tool for visual and mathematical analysis.
- Pure Resistor: V and I are in phase (phi = 0)
- Pure Inductor: Current lags voltage by pi/2
- Pure Capacitor: Current leads voltage by pi/2
- Impedance Z = sqrt(R^2 + (XL - XC)^2)
- Phase angle phi = tan^-1((XL - XC)/R)
Series LCR Resonance
Resonance occurs in an LCR circuit when the inductive reactance equals the capacitive reactance, forcing the circuit to act as a purely resistive load. This condition is crucial for tuning applications and signal processing in communication systems.
- Resonant condition: XL = XC
- Resonant frequency omega_r = 1/sqrt(LC)
- Circuit impedance is minimum (Z = R)
- Current is maximum at resonance
- Quality factor Q = (1/R)*sqrt(L/C)
Transformers
Transformers are static devices that use mutual induction to change the voltage level of AC power. They are governed by the turns ratio and the conservation of power principle, assuming ideal conditions with no energy loss.
- Turns ratio K = Ns/Np = Vs/Vp
- For ideal transformer: VsIs = VpIp
- Step-up: Ns > Np; Step-down: Ns < Np
- Core losses include eddy currents and hysteresis
- Efficiency eta = (Output Power / Input Power) * 100
Formula Sheet
I = I_m sin(omega*t)
V_rms = V_m / sqrt(2)
I_rms = I_m / sqrt(2)
XL = omega*L
XC = 1 / (omega*C)
P_avg = V_rms * I_rms * cos(phi)
cos(phi) = R / Z
omega_r = 1 / sqrt(LC)
Vs/Vp = Ns/Np
Exam Tip
Always draw a quick phasor diagram before writing your equations, as it acts as a geometric check to avoid sign errors in your final impedance calculation.
Common Mistakes
- Confusing phase relationships, specifically mixing up whether current leads or lags in capacitive vs inductive circuits.
- Forgetting to calculate RMS values instead of peak values when computing average power or heat dissipation.
- Neglecting to convert frequency (f) to angular frequency (omega = 2*pi*f) before calculating reactances.
More Revision Notes
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