Class 12 Physics · Original EZT practice
Alternating Current (Class 12 Chapter 7): summary and practice
Alternating current swings sinusoidally, so the chapter gives you a full toolkit: rms values for measuring it, reactances X_L and X_C for inductors and capacitors, the series LCR impedance triangle, resonance, the power factor, and the transformer. All questions are original EZT tutor practice following the chapter's own section order.
6 original worked examples, 6 fresh self-check questions and 4 mixed questions, with explained answers. These are not copied textbook exercises, an official chapter index or a full answer key. No affiliation with NCERT is claimed.
Official sources for topic and edition context, checked 21 October 2026:
1. AC quantities and rms values
Mains voltage swings as V = V_peak sin(omega t). The rms value is the DC-equivalent heating value: V_rms = V_peak/sqrt2, and the marked 220 V is already rms. At 50 Hz, omega = 2 pi nu is about 314 rad/s.
2. Resistor, inductor and capacitor on AC
A resistor keeps V and I in phase. An inductor makes current lag by 90 degrees with reactance X_L = 2 pi nu L. A capacitor makes current lead by 90 degrees with X_C = 1/(2 pi nu C) - rising with frequency for the inductor, falling for the capacitor.
3. Series LCR circuit
Phasors (rotating vectors) add the out-of-phase voltages: Z = sqrt(R^2 + (X_L - X_C)^2). The reactances fight each other, so X_L - X_C, never their sum, sets the impedance.
4. Resonance (7.6.2)
When X_L = X_C the impedance bottoms out at R and the current peaks. Resonant frequency nu = 1/(2 pi sqrt(LC)) - the principle behind tuning a radio.
5. Power factor and transformers
Average power is P = V I cos phi, with cos phi = R/Z the power factor; pure L or C burn no average power. A transformer steps voltage with the turns ratio Vs/Vp = Ns/Np, ideally conserving power.
Choose, solve, check, then try a fresh question.
Before calculating, read the method prompt and name the condition that makes it useful. Write your own attempt. Open the steps only when you need them, and use the check to catch a wrong sign, unit or interpretation. Finish with the fresh question before reading its answer.
Convert peak and rms
Choose the method: V_rms = V_peak/sqrt2 and omega = 2 pi nu.
EZT practice question
Indian mains reads 220 V at 50 Hz. Find the peak voltage and the angular frequency.
Show the worked solution
- V_peak = 220 x sqrt2 = 220 x 1.414.
- omega = 2 x pi x 50.
Answer: V_peak is about 311 V and omega is about 314 rad/s.
Check: The peak must exceed the rms - 311 > 220.
Watch for this: The nameplate 220 V is rms already - do not divide it by sqrt2 again.
Now try it yourself
Find the peak of a 110 V rms supply.
Check your answer
About 156 V.
110 x 1.414 = 155.5, about 156 V.
Drive an inductor
Choose the method: X_L = 2 pi nu L, then I = V/X_L.
EZT practice question
A 0.1 H inductor sits on a 220 V, 50 Hz supply. Find its reactance and the rms current.
Show the worked solution
- X_L = 2 x pi x 50 x 0.1 = 31.4 ohm.
- I = 220/31.4.
Answer: X_L = 31.4 ohm and I is about 7.0 A.
Check: More frequency or more L would raise X_L and lower the current - the inductor resists change.
Watch for this: Use rms with rms: pair the 220 V rms with an rms current.
Now try it yourself
Find X_L for a 25 mH inductor at 50 Hz (the chapter's own example).
Check your answer
7.85 ohm.
X_L = 2 x pi x 50 x 0.025 = 7.85 ohm.
Drive a capacitor
Choose the method: X_C = 1/(2 pi nu C).
EZT practice question
A 100 microfarad capacitor connects to a 50 Hz supply. Find its reactance.
Show the worked solution
- X_C = 1/(2 x pi x 50 x 100 x 10^-6).
- Denominator = 0.0314.
Answer: X_C is about 31.8 ohm.
Check: Bigger C or higher frequency lowers X_C - the capacitor passes AC more easily.
Watch for this: Convert microfarads first: 100 microfarad is 10^-4 F, not 100 F.
Now try it yourself
What happens to X_C when the frequency doubles?
Check your answer
It halves.
X_C is inversely proportional to frequency.
Solve a series LCR circuit
Choose the method: Z = sqrt(R^2 + (X_L - X_C)^2); I = V/Z; cos phi = R/Z.
EZT practice question
A series LCR has R = 30 ohm, X_L = 70 ohm and X_C = 30 ohm on 220 V. Find Z, the current, the power factor and the power consumed.
Show the worked solution
- Z = sqrt(30^2 + (70 - 30)^2) = sqrt(900 + 1600) = sqrt(2500) = 50 ohm.
- I = 220/50 = 4.4 A.
- cos phi = R/Z = 30/50 = 0.6.
- P = V I cos phi = 220 x 4.4 x 0.6 = 580.8 W.
Answer: Z = 50 ohm, I = 4.4 A, power factor 0.6 and P = 580.8 W.
Check: Cross-check with P = I^2 R = 4.4^2 x 30 = 580.8 W - same, because only R burns power.
Watch for this: Subtract the reactances - X_L and X_C point in opposite phase directions.
Now try it yourself
Repeat with R = 40, X_L = 60, X_C = 30 ohm: find Z and the power factor.
Check your answer
Z = 50 ohm, power factor 0.8.
Z = sqrt(40^2 + 30^2) = 50, and cos phi = 40/50 = 0.8.
Find the resonant frequency
Choose the method: nu = 1/(2 pi sqrt(LC)).
EZT practice question
An LCR circuit has L = 0.1 H and C = 100 microfarad. At what frequency does it resonate?
Show the worked solution
- LC = 0.1 x 10^-4 = 10^-5.
- sqrt(LC) = 3.16 x 10^-3.
- nu = 1/(2 x pi x 3.16 x 10^-3).
Answer: Resonance at about 50.3 Hz - nearly the mains frequency.
Check: At resonance X_L = X_C: 31.4 vs 31.8 ohm from the earlier examples - very close, as expected.
Watch for this: Watch the units: C in farads, answer in Hz.
Now try it yourself
If C is made 4 times smaller, what happens to the resonant frequency?
Check your answer
It doubles.
nu is proportional to 1/sqrt(C), and sqrt(4) = 2.
Step voltage with a transformer
Choose the method: Vs/Vp = Ns/Np for an ideal transformer.
EZT practice question
An ideal transformer has 1000 primary turns and 100 secondary turns, with 220 V on the primary. Find the secondary voltage.
Show the worked solution
- Vs = Vp x Ns/Np.
- Vs = 220 x 100/1000.
Answer: Vs = 22 V - a step-down of ten to one.
Check: Fewer secondary turns means lower voltage - and ideally the current steps UP tenfold to keep power equal.
Watch for this: An ideal transformer conserves power, not current - do not assume both V and I drop.
Now try it yourself
Same core, 220 V in, but 2000 secondary turns. Output?
Check your answer
440 V.
Vs = 220 x 2000/1000 = 440 V - now it steps up.
Try a mixed set
Choose a method or explanation before opening each answer.
1. V_rms from V_peak?
Show answer and reason
V_rms = V_peak/sqrt2.
Rms is the DC-equivalent heating value.
2. Inductive reactance?
Show answer and reason
X_L = 2 pi nu L.
Grows with frequency - inductors choke high frequencies.
3. Capacitive reactance?
Show answer and reason
X_C = 1/(2 pi nu C).
Falls with frequency - capacitors pass AC, block DC.
4. Series LCR impedance?
Show answer and reason
Z = sqrt(R^2 + (X_L - X_C)^2).
The reactances are 180 degrees out of phase with each other.
Try it yourself
Work these on paper before checking any notes. Answers are deliberately not shown here.
- A series LCR has R = 40, X_L = 60, X_C = 30 ohm. Find Z and the power factor.
- Find the reactance of a 25 mH inductor at 50 Hz.
- Find the peak voltage of a 110 V rms supply.
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Questions about this practice page
- Why does a capacitor block DC?
- X_C = 1/(2 pi nu C), and DC has nu = 0, so the reactance is infinite - after charging, no steady current flows. AC keeps charging and discharging the plates, so a current flows in the circuit.
- What is resonance in an LCR circuit?
- The frequency where X_L = X_C exactly cancel, leaving Z = R and the maximum possible current. It happens at nu = 1/(2 pi sqrt(LC)) and is how radios tune into one station.
- What is the power factor?
- cos phi = R/Z, the fraction of V x I that becomes real average power: P = V I cos phi. A pure inductor or capacitor has phi = 90 degrees and consumes zero average power.
- Does a transformer change the power?
- An ideal transformer conserves power: stepping voltage down steps current up by the same ratio. Real transformers lose a little to heating, flux leakage and core losses.
- Are these the NCERT exercise questions for Alternating Current (Class 12)?
- No. EZT pages are original practice following the chapter's section order - use them to prepare for the textbook exercises, not as a substitute for your book.