Alternating CurrentNEET Physics · Class 12 · NCERT Chapter 7

Introduction

Alternating current (AC) reverses direction many times per second. Indian household mains is 50 Hz: the current changes direction 100 times every second. This chapter covers how V and I behave through R, L and C in AC circuits, what happens when you combine them, and how transformers change voltages.

Expect 1 to 2 NEET questions. Favourites: RMS values, AC across a single inductor or capacitor (phase), impedance and resonance of series LCR, transformer ratios.

AC voltage and current

Standard sinusoidal AC:

V_0 and I_0 are peak values. omega = 2 pi f is angular frequency. Phase phi depends on the type of element.

RMS, peak and average values

Mean of sin(omega t) over a full cycle is zero, but the RMS value (which controls heating) is not:

Mean over a half-cycle (full-wave rectified) is $2V_0/\pi$. When NEET says "220 V mains", that means RMS, so the peak is V_0 = 220 sqrt(2) ≈ 311 V.

For a sinusoidal AC, peak V_0 is the maximum value. Mean over a full cycle is zero. RMS = V_0 / sqrt(2). Mean over a half-cycle = 2 V_0 / pi.

AC through a resistor

Voltage and current in phase. For $v=V_0\sin \omega t$:

Power dissipated: $P_{\text{avg}}=V_{\text{rms}}{I}_{\text{rms}}=V_{\text{rms}}^2/R$.

AC through a pure resistor: voltage and current are exactly in phase. No phase shift.

AC through an inductor

Voltage leads current by π/2:

X_L is inductive reactance, in ohms. Higher frequency means higher reactance (inductor blocks AC at high f). Average power consumed by an ideal inductor over a cycle is zero.

AC through an inductor: V leads I by π/2 (90°). Reactance X_L = ω L grows with frequency.

AC through a capacitor

Current leads voltage by π/2:

X_C is capacitive reactance. Higher frequency means LOWER reactance (capacitor passes AC at high f, blocks DC). Average power consumed by an ideal capacitor over a cycle is zero.

AC through a capacitor: I LEADS V by π/2 (90°). Reactance X_C = 1/(ω C) DROPS with frequency.

Memory hook: ELI the ICE man

In an inductor (L), E (voltage) leads I. In a capacitor (C), I leads E (voltage). ELI the ICE man.

Series LCR circuit

With R, L and C in series, total opposition (impedance):

Phase angle phi between V and I:

If X_L > X_C: voltage leads current (inductive). If X_C > X_L: voltage lags current (capacitive).

Series LCR: total opposition is the impedance Z. Phase angle phi between V and I depends on which reactance wins.

Resonance

At a special frequency, X_L = X_C, the reactances cancel, and Z reduces to R alone:

At resonance, current is maximum (V/R), and phase angle is zero. Quality factor Q measures the sharpness:

Used for tuning radios and TVs to a specific station.

At resonance, X_L = X_C. The reactive parts cancel; impedance equals R alone. Current is maximum at the resonance frequency.

Power in AC circuits

Average power over a full cycle:

cos φ is the power factor. For a pure resistor: cos φ = 1, all power is real. For a pure L or C: cos φ = 0, no real power. Wattless current: I_rms sin φ flows but does no real work; only the in-phase component I_rms cos φ delivers real power.

Transformer

Two coils linked by a common iron core. AC current in the primary creates a changing flux that induces an EMF in the secondary:

For an ideal (lossless) transformer, P_p = P_s, so:

Step-up: more turns on secondary, voltage rises but current falls. Step-down: opposite. Real transformers lose energy to copper resistance, hysteresis and eddy currents (use laminated cores to reduce).

Ideal transformer: turns ratio sets the voltage ratio. Power in = power out (no losses).

AC generator (brief)

A coil rotated in a magnetic field produces a sinusoidal EMF:

Slip rings carry the AC out to the external circuit. This is how power plants generate electricity at 50 Hz (or 60 Hz in some countries).

Worked NEET problems

Summary cheat sheet

• RMS: $V_{\text{rms}}=V_0/\sqrt{2}$.
• Inductor: V leads I by π/2. $X_L=\omega L$.
• Capacitor: I leads V by π/2. $X_C=1/(\omega C)$.
• LCR impedance: $Z=\sqrt{R^2+(X_L-X_C{)}^2}$.
• Phase: $\tan \varphi =(X_L-X_C)/R$.
• Resonance: ${\omega }_0=1/\sqrt{LC}$.
• Q-factor: $Q=(1/R)\sqrt{L/C}$.
• Power: $P=V_{\text{rms}}{I}_{\text{rms}}\cos \varphi$.
• Transformer: $V_s/V_p=N_s/N_p$, $I_s/I_p=N_p/N_s$.

Next: try the interactive widgets for AC through R/L/C, LCR impedance and transformer, or work through the 32 NEET PYQs with full solutions. To time yourself, take the free 10-question mock test.