Alternating Current — Class 12 MCQs with Answers

Alternating Current — important questions & MCQs with answers (Class 12 Physics)

6 solved questions from this chapter's difficulty levels, each with its answer and explanation. Tap an option to check yourself.

0 of 6 answered

1. Q1 of 6Easy

   Vrms = Vpeak ÷

   A2B√2CπD3
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   Answer: √2

   Explanation: For a sinusoid, V_rms = V₀/√2 ≈ 0.707V₀, since the mean of sin²θ over a cycle is ½. Dividing by 2 (a common slip) would underestimate rms by nearly 30%.

2. Q2 of 6Easy

   Capacitive reactance:

   AC/ωBωCCωLD1/(ωC)
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   Answer: 1/(ωC)

   Explanation: Capacitive reactance X_C = 1/(ωC) — it falls as frequency rises, opposite to an inductor's X_L = ωL. Swapping the two formulas is the classic mix-up here.

3. Q3 of 6Medium

   Transformer: N_p = 1000, N_s = 100, V_p = 220 V. V_s =

   A22 VB2200 VC110 VD440 V
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   Answer: 22 V

   Explanation: V_s = (N_s/N_p)V_p = (100/1000)(220) = 22 V — inverting the turns ratio (N_p/N_s) is what produces the tempting 2200 V distractor.

4. Q4 of 6Medium

   Assertion (A): A capacitor connected to an ac source is alternately charged and discharged as the current reverses every half cycle. Reason (R): Capacitive reactance has the same dimensions as resistance.

   ABoth A and R are true and R is the correct explanation of ABBoth A and R are true but R is not the correct explanation of ACA is true but R is falseDA is false but R is true
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   Answer: Both A and R are true but R is not the correct explanation of A

   Explanation: A is true: the current reverses each half cycle, so the capacitor charges and then discharges again and again. R is true, since capacitive reactance is measured in ohm, but it is about units and says nothing about charging and discharging, so it does not explain A.

5. Q5 of 6Hard

   Transformer works on principle of:

   ASelf-inductionBMutual inductionCResistanceDCapacitance
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   Answer: Mutual induction

   Explanation: A transformer transfers energy between two separate, magnetically-linked coils via a changing flux — this is mutual induction, distinct from a single coil's self-induction.

6. Q6 of 6Hard

   Assertion (A): A series RL circuit can be brought into resonance by choosing a suitable frequency of the ac source. Reason (R): In a series LCR circuit at resonance, the voltages across L and C are equal in magnitude and opposite in phase.

   ABoth A and R are true and R is the correct explanation of ABBoth A and R are true but R is not the correct explanation of ACA is true but R is falseDA is false but R is true
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   Answer: A is false but R is true

   Explanation: A is false: resonance needs both L and C, so that their voltages can cancel; an RL circuit has no capacitor and cannot resonate. R is true: at resonance XL = XC, so the voltages across L and C are equal and π out of phase.

Alternating Current notes: key concepts (Class 12 Physics)

Circuits driven by sinusoidal sources: RMS and average values, the behaviour of R, L and C individually with their phase relations, the series LCR circuit with impedance and phase angle, resonance and the quality factor, power and the power factor, and the transformer with its energy losses.

Alternating current

Current whose magnitude and direction vary sinusoidally with time. Indian mains supply is 220 V at 50 Hz.

RMS value

The steady direct current that would produce the same heating, equal to the peak value divided by √2. Every AC meter reads RMS, not peak.

Average value

Zero over a full cycle, since the positive and negative halves cancel exactly. Over a half cycle it is 2I₀/π.

AC through a resistor

Voltage and current stay exactly in phase, so a resistor behaves in AC just as it does in DC and dissipates full power.

AC through an inductor

Current LAGS voltage by 90°. The inductor opposes changes in current, offering inductive reactance that rises with frequency.

AC through a capacitor

Current LEADS voltage by 90°. Capacitive reactance falls with frequency, so a capacitor blocks DC and passes high-frequency AC.

Phasor diagram

Represents voltages and currents as rotating vectors, turning the phase algebra of an AC circuit into simple vector addition.

Series LCR circuit

The inductor and capacitor voltages are 180° out of phase and partially cancel, so their difference combines with the resistor voltage in quadrature.

Impedance

The total opposition to AC, combining resistance and net reactance in quadrature. It is measured in ohms but is frequency-dependent.

Phase angle

The angle by which the current leads or lags the voltage, set by the ratio of net reactance to resistance.

Resonance

Occurs when inductive and capacitive reactances cancel exactly. Impedance falls to its minimum R, and current reaches its maximum.

Quality factor

Measures the sharpness of the resonance peak. A high Q means a narrow bandwidth, which is exactly what a radio tuner needs.

Power in an AC circuit

The average power is V_rms I_rms cos φ, so the phase angle directly determines how much of the apparent power is actually delivered.

Power factor

The cosine of the phase angle, equal to R/Z. It is one for a purely resistive circuit and zero for a purely reactive one.

Wattless current

The component of current 90° out of phase with the voltage, which transfers no net power over a cycle however large it is.

Transformer

Changes AC voltage using mutual induction between two coils on a shared core. It works ONLY on AC, since DC produces no changing flux.