Class 12 Physics, Chapter 7 (NCERT). 15 questions by concept, 1 with pictures. Open “Show answer” for the answer and why.
How to teach this chapter · Common misconceptions & worked visual for this chapter
A nonzero sinusoidal current completes a full cycle through a resistor. Which pair of cycle averages is correct?
(a) Mean current zero; mean-square current positive
Positive and negative current cancel in the mean. Squared current is nonnegative and does not cancel.
An AC current has zero signed mean but gives the same average heating in a resistor as 3 A dc. What is its rms current?
(b) 3 amperes
RMS is defined by equal heating in the same resistor. Zero signed mean does not make the mean square zero.
An ideal capacitor has voltage v=Vm sinωt. Which current is consistent with i=C dv/dt?
(a) i=Im sin(ωt+π/2)
Differentiation gives i=ωCVm cosωt, which leads voltage by π/2.
In a pure capacitor circuit the sinusoidal voltage crosses zero while increasing. What is the current at that instant?
(c) Positive maximum
At the rising voltage zero crossing, dv/dt is maximum and positive. Hence i=C dv/dt is at positive maximum.
A pure inductor draws half its original rms current after only the source frequency is changed. The rms source voltage is unchanged. How did the frequency change?
(d) It doubled
At fixed V and L, I∝1/f. Halving I requires doubling f.
An ideal inductor has voltage v=Vm sinωt in sinusoidal steady state. Which current time dependence is correct?
(b) i=Im sin(ωt-π/2)
Integrating v=L di/dt gives i=-(Vm/ωL)cosωt. This is a quarter-cycle lag.
The diagram gives the three rms voltage phasors of a series LCR circuit, with current used as the phase reference. What is the source rms voltage?
(c) 50 V
VL and VC oppose, leaving 40 V perpendicular to VR. The source magnitude is sqrt(VR²+(VL-VC)²).
In a series LCR circuit current leads the source voltage by a nonzero angle smaller than 90°. What relation between reactances follows?
(b) XC>XL
A leading current indicates net capacitive reactance. Under i=Im sin(ωt+φ), tanφ=(XC-XL)/R is positive.
A series LCR circuit has rms voltages VL=VC=200 V and VR=100 V. A student reports source voltage 500 V by adding the meter readings. What source voltage follows from their phases?
(b) 100 V
Inductive and capacitive voltages cancel as phasors. The source equals VR even though both reactive meter readings are large.
To halve the resonance angular frequency of a circuit while keeping L unchanged, how must C change?
(c) Increase to 4C
Since ω0²LC=1, halving ω0 requires four times the capacitance.
A series LCR circuit is at resonance with nonzero resistance. Which pair describes its impedance and phase difference?
(b) Z=R; voltage and current are in phase
Only the reactive voltage contributions cancel. The resistor remains, giving finite impedance and zero phase difference.
An ideal inductor has nonzero sinusoidal voltage and current. Its instantaneous power is negative during part of a cycle. What does that negative power mean?
(d) Stored magnetic energy is being returned to the source
A pure inductor stores and returns magnetic energy. Negative instantaneous power is energy return, not resistive dissipation.
A sinusoidal load has rms voltage 100 V, rms current 5 A and power factor 0.6. What is its average power?
(a) 300 W
Real power is VI cosφ. With power factor 0.6, only three fifths of the apparent power is dissipated.
An ideal transformer delivers rms voltage 440 V and current 5 A to a resistor. The primary rms voltage is 220 V. What primary current is drawn?
(a) 10 amperes
Output power is 440×5=2200 W. The input current is 2200/220=10 A; the lower-voltage side carries more current.
A conventional transformer primary is connected to a steady dc source. After the switching transient, what sustained secondary emf is produced by the steady core flux?
(b) Zero emf
Faraday induction requires changing flux. A steady flux has dΦ/dt=0 and gives no sustained secondary emf.
Wrong
A resistor on AC cannot heat because the current averages to zero.
Why it feels right. I assume positive and negative half cycles cancel their heating.
Right
Resistive heating depends on I²R, which is positive for nonzero current in either direction.
Worked example
