All Important Formulas of Alternating Current (Quick Revision Summary)
Physics · Alternating Current · NEET
Here is the full formula sheet for Alternating Current. The five you must never forget are: RMS value V_rms = V0/root2 = 0.707 V0, inductive reactance X_L = 2*pi*f*L, capacitive reactance X_C = 1/(2*pi*f*C), impedance of series LCR Z = root(R^2 + (X_L - X_C)^2), and average power P = V_rms*I_rms*cos(phi). Memory hook: "RRIP-T" = RMS, Reactance, Impedance, Power, Transformer, the five families every NEET AC question comes from.
The AC formula sheet grouped into five families (RMS, reactance, impedance, power, transformer). Reactances feed impedance, impedance feeds current and phase, and current plus phase feed power. Almost every NEET AC numerical is one of these five.
Your doubts, answered
Which AC formula do I actually use in a numerical, peak or RMS?
Read the given value. If the source is written as V = V0 sin(wt), the number in front is the PEAK value V0. If the source is quoted like '220 V, 50 Hz supply', that number is the RMS value. Rule for NEET: find impedance Z first, then use I_peak = V0/Z when you started from V0, or I_rms = V_rms/Z when you started from the RMS number. For power always use RMS: P = V_rms*I_rms*cos(phi). Never mix a peak voltage with an RMS current in the same line.
What is the difference between reactance and impedance in the formula sheet?
Reactance is the opposition of ONE reactive part alone: inductor X_L = 2*pi*f*L, capacitor X_C = 1/(2*pi*f*C). Impedance Z is the TOTAL opposition of the whole series circuit combined: Z = root(R^2 + (X_L - X_C)^2). So reactance is a building block; impedance is the final answer that replaces resistance in Ohm's law for AC: I = V/Z.
What are the resonance formulas I need at exam time?
At resonance in a series LCR circuit X_L = X_C. From this you get the resonant frequency f0 = 1/(2*pi*root(LC)) (in hertz) or omega0 = 1/root(LC) (in rad/s). At resonance impedance is minimum Z = R, current is maximum I = V/R, and power factor cos(phi) = 1. Sharpness is the quality factor Q = (1/R)*root(L/C) = omega0*L/R.
What is the transformer formula and which way is step-up?
For an ideal transformer V_s/V_p = N_s/N_p = I_p/I_s. Voltage follows turns, current is opposite. If N_s > N_p it is step-UP (voltage rises, current falls). Power is conserved: V_p*I_p = V_s*I_s. To find primary current from a lamp rating use I_p = Power/V_primary.
What is the formula for average power and power factor?
Average power P = V_rms*I_rms*cos(phi), where cos(phi) is the power factor. For a series LCR circuit cos(phi) = R/Z = R/root(R^2 + (X_L - X_C)^2). A pure resistor has cos(phi) = 1 (full power). A pure inductor or capacitor has cos(phi) = 0, so its average power is zero (wattless current).
⚠️ The NEET trap ✗ Treating 220 V from a '220 V, 50 Hz mains' as the peak value V0 and writing I_peak = 220/Z. ✓ A quoted supply voltage like 220 V is the RMS value. So V0 = root2 * 220 = 311 V. Use I_rms = 220/Z for RMS current, and only multiply by root2 if the question asks for the PEAK current. Match RMS with RMS and peak with peak. 🧠 The '220 V means peak' mistake costs a mark almost every year.
Real NEET questions
2026
An ac voltage V = 220 sin(2x10^3 t) V is applied to a series LCR circuit with L = 10 mH, C = 25 uF, R = 100 ohm. The current amplitude in the circuit is:
A · 2.2 A ✓
B · 5.5 A
C · 11.0 A
D · 22.0 A
Solution: Step 1 (read the source): V = 220 sin(2x10^3 t), so peak voltage V0 = 220 V and omega = 2x10^3 rad/s.
Step 2 (reactances): X_L = omega*L = (2x10^3)(10x10^-3) = 20 ohm. X_C = 1/(omega*C) = 1/[(2x10^3)(25x10^-6)] = 1/(0.05) = 20 ohm.
Step 3 (impedance): X_L - X_C = 20 - 20 = 0, so the circuit is at resonance. Z = root(R^2 + 0) = R = 100 ohm.
Step 4 (current amplitude): I0 = V0/Z = 220/100 = 2.2 A. Answer (A).
2020
A series LCR circuit is connected to an ac source. When L is removed the phase difference between current and voltage is pi/3. When instead C is removed the phase difference is again pi/3. The power factor of the circuit is:
A · 1.0 ✓
B · -1.0
C · Zero
D · 0.5
Solution: Step 1 (L removed, only R and C): tan(pi/3) = X_C/R, so X_C = R*root3.
Step 2 (C removed, only R and L): tan(pi/3) = X_L/R, so X_L = R*root3.
Step 3 (full circuit): X_L = X_C = R*root3, so net reactance X_L - X_C = 0. This is the resonance condition.
Step 4 (power factor): cos(phi) = R/Z = R/root(R^2 + 0) = 1. Answer (A). Equal reactances cancel, so the circuit behaves purely resistive.
2016
An inductor 20 mH, a capacitor 100 uF and a resistor 50 ohm are connected in series across a source of emf V = 10 sin(314 t). The power loss in the circuit is:
A · 2.74 W
B · 0.43 W
C · 0.79 W ✓
D · 1.13 W
Solution: Step 1 (read source): V0 = 10 V so V_rms = 10/root2 = 7.07 V; omega = 314 rad/s.
Step 2 (reactances): X_L = omega*L = 314 x 20x10^-3 = 6.28 ohm. X_C = 1/(omega*C) = 1/(314 x 100x10^-6) = 31.85 ohm.
Step 3 (impedance): X_L - X_C = 6.28 - 31.85 = -25.57 ohm. Z = root(50^2 + 25.57^2) = root(2500 + 654) = root(3154) = 56.2 ohm.
Step 4 (power): P = (V_rms^2/Z^2)*R = (7.07^2/56.2^2) x 50 = (50/3158) x 50 = 0.79 W. Answer (C).
Solved Alternating Current NEET PYQs
Try the real previous-year questions from this chapter — each with the answer and a full solution.
V_rms = V0/root2 = 0.707 V0 and I_rms = I0/root2 = 0.707 I0. The peak is root2 times the RMS. This only holds for a pure sine wave, which is what NEET always assumes.
How does reactance change with frequency?
Inductive reactance rises with frequency, X_L = 2*pi*f*L (an inductor blocks high frequency). Capacitive reactance falls with frequency, X_C = 1/(2*pi*f*C) (a capacitor blocks DC where f = 0 and passes high frequency).
What is the phase angle formula for a series LCR circuit?
tan(phi) = (X_L - X_C)/R. If X_L > X_C the current lags (inductive). If X_C > X_L the current leads (capacitive). If X_L = X_C the phase angle is zero, which is resonance.
What is wattless current?
It is the current component that is 90 degrees out of phase with voltage, so it carries zero average power. A pure inductor or pure capacitor has cos(phi) = 0, so all its current is wattless and it dissipates no energy over a cycle.
Which AC formulas are highest yield for NEET?
By past papers, the top families are series LCR impedance and current, resonant frequency f0 = 1/(2*pi*root(LC)), power factor cos(phi) = R/Z, average power P = V_rms*I_rms*cos(phi), and the transformer relations. Almost every AC question each year comes from these five.
