AC

🟢 Lite — Quick Review (1h–1d)

Rapid summary for last-minute revision before your exam.

Alternating current theory is a high-weightage topic in NEET Physics. For rapid revision, remember the basic alternating emf equation ε = ε₀ sin(ωt), where ε₀ is the peak value and ω is the angular frequency. The RMS (root mean square) values are essential: ε_rms = ε₀/√2, V_rms = V₀/√2, and I_rms = I₀/√2. For a series LCR circuit, the impedance Z = √(R² + (ωL − 1/ωC)²). Resonance occurs when ωL = 1/ωC, giving the resonant angular frequency ω₀ = 1/√(LC). The quality factor Q = ω₀L/R = 1/(ω₀CR) measures the sharpness of resonance. In transformers, the turns ratio gives V_s/V_p = N_s/N_p. The average power in an AC circuit is P_avg = V_rms I_rms cosφ, where cosφ is the power factor. Faraday’s law gives the induced emf ε = −dΦ/dt, and Lenz’s law determines the direction. Self-induction produces ε = −L(dI/dt), and the energy stored in an inductor is U = ½LI². Remember that British English spelling requires words such as “behaviour,” “centre,” and “analyser.” In NEET examinations, students often lose marks by confusing RMS values with peak values, so ensure you know when to use which.

🟡 Standard — Regular Study (2d–2mo)

For students who want genuine understanding…

Phasor diagrams are essential for understanding AC circuits. The voltage across a resistor VR is in phase with the current I. The voltage across an inductor VL leads the current by 90°. The voltage across a capacitor VC lags the current by 90°. These three voltages are represented as perpendicular phasors, and the applied voltage is their phasor sum. The impedance triangle is derived from these relationships: Z² = R² + (X_L − X_C)², and tanφ = (X_L − X_C)/R. The power triangle shows the relationship between true power P (in watts), reactive power Q (in VAR), and apparent power S (in VA), where cosφ = P/S = R/Z.

At resonance ω₀ = 1/√(LC), the inductive and capacitive reactances cancel, giving Z = R (minimum impedance) and I = I_max (maximum current). A remarkable feature of resonance is that the voltages across the inductor and capacitor can far exceed the applied voltage: V_L = I₀ω₀L = QV_applied and V_C = I₀/(ω₀C) = QV_applied. This voltage magnification factor equals the quality factor Q. The bandwidth Δω = ω₀/Q defines the range of frequencies over which the power falls to half its maximum value. The half-power frequencies ω₁ and ω₂ satisfy the condition that the current is I_max/√2. Larger Q means a narrower bandwidth and sharper resonance, which is important for radio tuning circuits where selectivity is desired. For power distribution systems, a lower Q gives a broader resonance curve, allowing the system to handle a wider frequency range.

The choke coil is an iron-core inductor with large self-inductance L and small resistance R. It is used to limit AC current while dissipating very little power (unlike a resistor), making it energy-efficient. In DC circuits at steady state (after a long time), an inductor acts as a short circuit because the current becomes constant and dI/dt = 0, so the induced emf is zero. In AC circuits, the inductive reactance X_L = ωL opposes current flow. A capacitor blocks DC (open circuit at ω = 0, since X_C → ∞) but allows AC to pass with reactance X_C = 1/ωC.

Transformers transfer electrical energy between circuits at different voltages. An ideal transformer has P_in = P_out = V_p I_p = V_s I_s, giving V_s/V_p = N_s/N_p = I_p/I_s. The efficiency η = (P_out/P_in) × 100%. Practical transformers have losses: copper losses I²R in the windings, iron or hysteresis losses in the core, and eddy current losses. Laminating the core reduces eddy current losses. Transformers are rated in kVA because the rating is independent of power factor; a 100 kVA transformer can deliver 100 kW at unity power factor or 100 kVAR at zero power factor. NEET numerical problems frequently test the relationship between turns ratio, voltage ratio, and current ratio, as well as power calculations in transformers.

🔴 Extended — Deep Study (3mo+)

Comprehensive theory…

The phasor method for AC analysis can be derived rigorously using complex numbers. Representing the current as I = I₀e^(jωt) and voltages as complex impedances Z_R = R, Z_L = jωL, and Z_C = 1/(jωC) = −j/(ωC), the total impedance is Z = R + j(ωL − 1/ωC). The magnitude |Z| = √(R² + (ωL − 1/ωC)²) and the phase angle φ = tan⁻¹((ωL − 1/ωC)/R). For pure R, V = IR with φ = 0; for pure L, V = IX_L with φ = +90°; for pure C, V = IX_C with φ = −90°. In the series LCR circuit, the voltage across each element is determined by the current common to all three.

Power in the series LCR circuit is P_avg = V_rms I_rms cosφ = I_rms² R. The quality factor Q can be derived from the bandwidth definition. At the half-power points, power equals ½ P_max, so current equals I_max/√2. The impedance at this point is Z = √2 R, which gives (X_L − X_C)² = R². Solving for the half-power frequencies yields Δω = ω₀/Q, so Q = ω₀/Δω = ω₀L/R. For a series resonant circuit, Q also equals Q = 1/(ω₀CR). High Q indicates sharp resonance with a narrow bandwidth, ideal for radio receivers where selectivity between stations is required. Low Q indicates broad resonance, suitable for power distribution where a range of frequencies must be handled.

Choke coils exploit the property that a large inductance opposes changes in current without dissipating significant power. In radio frequency circuits, choke coils block AC while allowing DC to pass through. Series resonance is used in radio tuning circuits to select a specific frequency from many broadcast signals. Parallel resonance (anti-resonance) produces very high impedance at resonance, useful in band-stop filters to block specific frequencies. Transformer equivalent circuits model real transformers with referred resistances and reactances, including the magnetising branch. Voltage regulation is defined as (V_no-load − V_full-load)/V_full-load × 100%, measuring how much the voltage drops under load. Good regulation means low voltage drop.

The auto-transformer has a single winding with a variable tapping point, providing variable output voltage. It is more efficient than a two-winding transformer for small voltage transformations because it uses the same winding for both primary and secondary. The step-up or step-down ratio is simply the turns ratio N_s/N_p. The AC generator or alternator operates on the principle of electromagnetic induction: a coil of N turns rotating in a uniform magnetic field with angular velocity ω produces an emf ε = NBAω sin(ωt), where A is the area of the coil and B is the magnetic flux density. Three-phase AC systems supply power using three alternating currents displaced by 120° in phase. For three-phase balanced loads, the total power is P = √3 V_L I_L cosφ, where V_L and I_L are the line voltage and current.

Magnetic energy density in a magnetic field is u = B²/(2μ₀). Mutual induction between two coils gives M = k√(L₁L₂), where k is the coupling coefficient. The dot convention indicates the relative polarity of induced voltages: when the current enters the dotted terminal of one coil, the induced emf at the dotted terminal of the other coil is positive. In NEET and JEE previous year questions, common traps include confusing RMS with peak values (especially in voltage magnification at resonance), using the wrong resonant frequency formula when resistance is significant, and forgetting power factor correction using capacitors to improve cosφ. In DC circuits with an inductor, the current builds up exponentially as I = I_max(1 − e^(−tR/L)), with the time constant τ = L/R. For a charging capacitor in an RC circuit, the time constant is τ = RC.