Alternating Current formulas

Class 12 physics formula sheet for NEET and JEE: the key equations of NCERT chapter 7, the special cases questions are built on, and diagrams where they help.

23 formulas7 sectionsClass 12 · Chapter 72 of 7 sections free

By Sreeraj P, M.Sc Physics · 10+ years teaching NEET and JEE

Most used formulasOther formulas and cases

1Alternating quantities

$$i=i_0\sin(\omega t+\phi),\qquad \omega=2\pi f=\frac{2\pi}T$$

$$\begin{array}{l}\displaystyle i=i_0\sin(\omega t+\phi)\\[6pt]\displaystyle \omega=2\pi f=\frac{2\pi}T\end{array}$$

Peak (amplitude) reached twice per cycle. Indian mains: 220 V rms, 50 Hz ($V_0\approx311$ V).

$$I_{\text{rms}}=\frac{I_0}{\sqrt2}=0.707I_0,\qquad I_{\text{avg}}(\text{half cycle})=\frac{2I_0}{\pi}=0.637I_0$$

$$\begin{array}{l}\displaystyle I_{\text{rms}}=\frac{I_0}{\sqrt2}=0.707I_0\\[6pt]\displaystyle I_{\text{avg}}(\text{half cycle})=\frac{2I_0}{\pi}=0.637I_0\end{array}$$

Average over a full cycle = 0. Meters read rms; rms = the DC giving the same heating. Form factor $=\dfrac{I_{\text{rms}}}{I_{\text{avg}}}=1.11$.

$$I_{\text{rms}}=\sqrt{\frac1T\int_0^Ti^2\,dt}$$

General definition. DC $a$ + AC $b\sin\omega t$: $\sqrt{a^2+b^2/2}$. Square wave: $I_0$; triangular/saw-tooth: $I_0/\sqrt3$; half-wave rectified: $I_0/2$ (avg $I_0/\pi$).

AC is more dangerous (peak exceeds rms) and flows mostly near the surface (skin effect → stranded wires). Only DC for electroplating.

2Single elements

	Resistor	Inductor	Capacitor
Opposition	$R$	$X_L=\omega L$	$X_C=\dfrac1{\omega C}$
Phase	$i$ in phase with $v$	$i$ lags by $\pi/2$	$i$ leads by $\pi/2$
Frequency	independent	$X_L\propto f$ (DC: 0)	$X_C\propto1/f$ (DC: ∞)
Average power	$V_{\text{rms}}I_{\text{rms}}$	0	0

Memory: ELI the ICE man – E before I in L; I before E in C.

5 more sections and 18 formulas in the full chapter

3Series circuits4 formulas · 1 diagram
4Power in AC circuits4 formulas
5Resonance5 formulas · 1 diagram
6LC oscillations3 formulas · 1 case table
7Transformer2 formulas

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