Alternating Current Short Notes for JEE Main: Revision Notes PDF

AC voltage and current

Sinusoidal AC

8× asked, last 2025

i = I_0\sin(\omega t+\phi),\qquad \omega = 2\pi f = \frac{2\pi}{T}

The number before sin is the peak; the number with

t

\omega

, not

f

. Indian mains: 50 Hz, so

T=20

ms.

t

i

T/4

T/2

I_0

I_0/2

T/8

T/6

peakrms

Time depends only on phase: zero to peak

T/4

; rms to peak

T/8

; half-peak to peak

T/6

Quick method. Timing questions depend only on phase: $\Delta t=\Delta\theta/\omega$ . Zero to peak takes $T/4$ , peak to rms $T/8$ , half-peak to peak $T/6$ . The voltage, $R$ and the rating do not matter.

Peak, rms and average values

11× asked, last 2025

I_{\text{rms}}=\frac{I_0}{\sqrt2},\qquad \bar I_{\text{half cycle}}=\frac{2I_0}{\pi},\qquad \bar I_{\text{full cycle}}=0

Sine waves only. Meters, ratings and 220 V mains are rms unless 'peak' is said. Heat and power use rms.

\omega t

i

\pi

2\pi

I_0

I_0/\sqrt2

(rms)mean

2I_0/\pi

Shaded half cycle: area

2I_0/\omega

, so the mean is

2I_0/\pi

; over a full cycle the mean is 0

Any wave: $\langle i\rangle=(1/T)\int i\,dt$ . Half-wave rectified $I_0/\pi$ ; full-wave $2I_0/\pi$ (rms $I_0/\sqrt2$ ). Over a half cycle: square $I_0$ , triangular $I_0/2$ . DC + AC: $I_{\text{dc}}$ .
Not a second $\sqrt2$ . Convert between peak and rms exactly once. In $E_0\sin\omega t$ the coefficient is already the peak; an ammeter shows $I_0/\sqrt2$ ; a rated current $P/V$ is rms, so the peak is $\sqrt2$ times it.
Not the peak value in $I^2Rt$ . Heating uses $I_{\text{rms}}^2$ , so an AC of peak $I_0$ gives half the heat of a steady DC $I_0$ in the same resistor.

rms of any waveform

7× asked, last 2026

I_{\text{rms}}=\sqrt{\langle i^2\rangle}=\sqrt{\frac1T\int_0^T i^2\,dt},\qquad I_{\text{rms}}=\sqrt{I_{\text{dc}}^2+\frac{I_0^2}{2}}

Average the square over one period, then take the root. Second form: a DC level plus a sine of peak

I_0

Waveform (peak $I_0$ )	rms
Sine	$I_0/\sqrt2$
Square $\pm I_0$	$I_0$
Triangle or ramp	$I_0/\sqrt3$
Half-wave rectified	$I_0/2$
Full-wave rectified	$I_0/\sqrt2$

The $1/\sqrt2$ is for sines only. Square wave $\pm I_0$ : rms $=I_0$ . Linear ramp or triangular wave of peak $I_0$ : $I_0/\sqrt3$ . Half-wave rectified sine: $I_0/2$ .
Not $I_{\text{dc}}+I_0/\sqrt2$ or $I_1+I_2$ . Mean squares add only if cross terms average to zero (DC + sine; sines $90^\circ$ apart or of different $\omega$ ): $I_1\sin\omega t+I_2\cos\omega t$ has rms $\sqrt{(I_1^2+I_2^2)/2}$ .
Quick method. Same- $\omega$ sines with phase gap $\delta$ : add as phasors, $I_0=\sqrt{I_1^2+I_2^2+2I_1I_2\cos\delta}$ ( $\sqrt{I_1^2+I_2^2}$ at $\delta=90^\circ$ ), then rms $=I_0/\sqrt2$ .

Practise Alternating Current questions as you read. Free, and you can start without signing up.

Practise Alternating Current

18 more concepts in 5 topics

AC circuits: R, L, C; Series RLC circuit; Resonance, Q-factor and LC oscillations; Power in AC circuits; and Transformers. Read the first part free. Sign in free with Google to read the rest and download the PDF.

AC circuits: R, L, C

Phasors5×
Phase in pure R, L and C8×
Inductive reactance10×
Capacitive reactance6×
Also remember2

Series RLC circuit

Impedance of series LCR19×
Phase angle in series LCR12×
Voltages add as phasors4×
RL and RC circuits14×

Resonance, Q-factor and LC oscillations

Series resonance33×
Quality factor8×
LC oscillations5×

Power in AC circuits

Average power15×
Power factor12×
Wattless current4×
Choke coil and rated lamps4×

Transformers

Ideal transformer6×
Efficiency of a real transformer2×
Losses and power transmission

Practise Alternating Current next

About 135 past JEE Main questions from this chapter, with instant answer checking and step-by-step solutions where available. Free, and you can start without signing up.

Practise Alternating Current

Also free on PrepWiser

Alternating Current formula sheet2 pages, every formula with when it applies
Alternating Current PYQ PDF with answer keyJEE Main questions from this chapter, ready to print
Daily Arena10 questions from one chapter, every day

Spotted a mistake? Write to support@prepwiser.in and we will fix it in the next version.

Version 1, October 2026. Free to share for study, as it is. Please don't sell it or remove the PrepWiser name.

Alternating Current revision notes

AC voltage and current

18 more concepts in 5 topics

AC circuits: R, L, C

Series RLC circuit

Resonance, Q-factor and LC oscillations

Power in AC circuits

Transformers

Practise Alternating Current next

Also free on PrepWiser

Downloading Alternating Current revision notes (PDF)

Alternating Current revision notes

1AC voltage and current3 concepts

18 more concepts in 5 topics

2AC circuits: R, L, C4 concepts

3Series RLC circuit4 concepts

4Resonance, Q-factor and LC oscillations3 concepts

5Power in AC circuits4 concepts

6Transformers3 concepts

Practise Alternating Current next

Also free on PrepWiser

AC voltage and current

AC circuits: R, L, C

Series RLC circuit

Resonance, Q-factor and LC oscillations

Power in AC circuits

Transformers