Class 12 Physics · NCERT notes for NEET

Alternating Current: NCERT Notes, Formulas and Tricks for NEET

How resistors, inductors and capacitors behave with sinusoidal voltage, series LCR resonance, AC power and transformers. NEET usually asks one or two questions from it, mostly quick numericals on reactance, impedance, resonance and power factor.

1. AC voltage applied to R, L and C
2. Series LCR circuit and resonance 🔒
3. Power in AC circuits 🔒
4. Transformers 🔒

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Open the interactive version (simulations and tap-to-answer quick checks).

Topic 1

AC voltage applied to R, L and C

The 220 V written on your wall socket is not the peak: the voltage actually swings between +311 V and −311 V fifty times every second.

An AC source gives $v = v_{m} sin ω t$ ; $v_{m}$ is the peak (amplitude) and $ω = 2 π ν$ . Indian mains: $ν = 50$ Hz, so $ω \approx 314 rad s^{- 1}$ .
RMS (effective) value: the steady current that gives the same heat in a resistor over a full cycle. $I = i_{m} / 2 \approx 0.707 i_{m}$ , $V = v_{m} / 2$ .
Average of a sine current over a full cycle is zero. Over a half cycle it is $2 i_{m} / π \approx 0.637 i_{m}$ .
AC meters read rms values. The 220 V supply is rms, so the peak is $2202 \approx 311$ V.
Pure resistor: $i = (v_{m} / R) sin ω t$ , in phase with $v$ . Heating goes as $i^{2}$ , so the average power is not zero.
Pure inductor: $i$ lags $v$ by $π /2$ (a quarter cycle). Inductive reactance $X_{L} = ω L$ rises with frequency; for DC $X_{L} = 0$ .
Pure capacitor: $i$ leads $v$ by $π /2$ . Capacitive reactance $X_{C} = 1/ (ω C)$ falls with frequency; for DC it is infinite, so C blocks DC.
Reactance is measured in ohm like resistance, but it stores and returns energy instead of turning it into heat.
Phasors are arrows that rotate anticlockwise at $ω$ ; the vertical projection gives the instantaneous value. The angle between $V$ and $I$ phasors is the phase difference.
Average power over a cycle is zero in a pure L and in a pure C: energy stored in one quarter cycle is given back in the next.

The orange line is the rms value 0.707\,i_m. The + and − areas cancel, so the full-cycle average is zero; only the half-cycle average is 0.637\,i_m. — The orange line is the rms value $0.707 i_{m}$ . The + and − areas cancel, so the full-cycle average is zero; only the half-cycle average is $0.637 i_{m}$ .

In L the current peaks T/4 after the voltage (lags by 90°); in C it peaks T/4 before (leads). The phasors show the same thing as a right angle. — In L the current peaks $T /4$ after the voltage (lags by $90°$ ); in C it peaks $T /4$ before (leads). The phasors show the same thing as a right angle.

X_L grows in a straight line with nu, X_C falls as 1/nu, R does not change. Where the two reactance curves cross is the resonant frequency nu_0. — $X_{L}$ grows in a straight line with $ν$ , $X_{C}$ falls as $1/ ν$ , $R$ does not change. Where the two reactance curves cross is the resonant frequency $ν_{0}$ .

Formulas

$I = \frac{i _{m}}{2}, V = \frac{v _{m}}{2}$
rms values from peak values
$i_{a v} = \frac{2 i _{m}}{π} \approx 0.637 i_{m}$
mean value over a half cycle (full cycle gives 0)
$X_{L} = ω L = 2 π ν L$
inductive reactance in ohm
$X_{C} = \frac{1}{ω C} = \frac{1}{2 π ν C}$
capacitive reactance in ohm
$i = \frac{v _{m}}{X _{L}} sin (ω t - \frac{π}{2})$
pure inductor: current lags
$i = \frac{v _{m}}{X _{C}} sin (ω t + \frac{π}{2})$
pure capacitor: current leads

Tips, tricks and hacks

ELI the ICE manE-L-I: in L, voltage (E) comes before current (I). I-C-E: in C, current comes before voltage. One word answers every lead/lag question.

Frequency scaling

X_{L} \propto ν

X_{C} \propto 1/ ν

. If

X_{C} = 40 Ω

at 50 Hz, then at 200 Hz it is

40/4 = 10 Ω

. No need to find C.

Peak, rms, average ladderPeak

\times 0.707

= rms; peak

\times 0.637

= half-cycle average. For 311 V peak: rms 220 V, half-cycle average about 198 V.

DC limit checkPut

ω = 0

X_{L} = 0

(L is just a wire) and

X_{C} = \infty

(open circuit). Any answer that lets steady DC pass through a capacitor is wrong.

Common mistakes

✗ Taking 220 V mains as the peak value.

✓ 220 V is rms; the peak is $2202 \approx 311$ V.

✗ Saying the average value of AC is $0.637 i_{m}$ .

✓ That is for a half cycle. Over a full cycle the average is exactly zero.

✗ In an inductor the current leads the voltage.

✓ The inductor opposes change of current, so current builds up late: it lags by $π /2$ .

✗ Reactance wastes power like resistance because both are in ohm.

✓ Pure L and C only store and return energy; average power in them is zero.

NEET traps

NEET gives $i = 10 sin (100 π t)$ and asks the rms value or frequency: rms $= 10/ 2 \approx 7.07$ A and $ν = 100 π /2 π = 50$ Hz, not 100 Hz.

Doubling frequency doubles $X_{L}$ but halves $X_{C}$ ; options often swap the two.

"A capacitor allows AC but blocks DC" is TRUE; "an inductor blocks DC" is FALSE (it offers zero reactance to steady DC).

Quick check: A

\frac{1}{π}

H inductor is connected to a 220 V, 50 Hz supply (neglect its resistance). The rms current is

2.2 A
1.1 A
3.1 A
4.4 A

Answer: A. $X_{L} = 2 π \times 50 \times \frac{1}{π} = 100 Ω$ , so $I = 220/100 = 2.2$ A.

Topic 2 · 🔒

Series LCR circuit and resonance

Key points, graphs, every formula, tricks, common mistakes and NEET traps for this topic are inside Dhruv.

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Topic 3 · 🔒

Power in AC circuits

Key points, graphs, every formula, tricks, common mistakes and NEET traps for this topic are inside Dhruv.

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Topic 4 · 🔒

Transformers

Key points, graphs, every formula, tricks, common mistakes and NEET traps for this topic are inside Dhruv.

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Practise Alternating Current questions

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