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Alternating Current — NEET & JEE MCQs with answers
Alternating current (AC) circuits involve voltages and currents that vary sinusoidally with time. The chapter covers the behaviour of resistors, inductors and capacitors individually under AC, the combined series LCR circuit including resonance, the concept of power factor, and the working of transformers. AC is preferred over DC for transmission because voltages can be stepped up or down efficiently using transformers.
Topics in this chapter
- 7.1 Introduction
- 7.2 AC Voltage Applied to a Resistor
- 7.3 Representation of AC Current and Voltage by Rotating Vectors — Phasors
- 7.4 AC Voltage Applied to an Inductor
- 7.5 AC Voltage Applied to a Capacitor
- 7.6 AC Voltage Applied to a Series LCR Circuit
- 7.7 Power in AC Circuit: The Power Factor
- 7.8 Transformers
Free practice questions
A $25\ \mu\text{F}$ capacitor is across an ac source of peak voltage $283\ \text{V}$ and frequency $50\ \text{Hz}$. The peak current is about:
- A. $2.22\ \text{A}$
- B. $1.11\ \text{A}$
- C. $1.57\ \text{A}$
- D. $4.45\ \text{A}$
Show answer
Answer: A — $X_C=1/(2\pi fC)\approx 127\ \Omega$; $i_m=v_m/X_C=283/127\approx 2.22\ \text{A}$.
NCERT Class 12 Physics Ch 7 ("A 15.0 µF capacitor is connected to a 220 V, 50 Hz source")
A series LCR circuit ($L=0.8\ \text{H}$, $C=5\ \mu\text{F}$) resonates at a frequency $\nu_0$ of nearly:
- A. $39.8\ \text{Hz}$
- B. $79.6\ \text{Hz}$
- C. $159\ \text{Hz}$
- D. $500\ \text{Hz}$
Show answer
Answer: B — $\nu_0=\dfrac{\omega_0}{2\pi}=\dfrac{1}{2\pi\sqrt{LC}}\approx79.6\ \text{Hz}$.
NCERT Class 12 Physics Ch 7 ("is called the resonant frequency")
The everyday example given in the text of taking advantage of a special property of ac circuits is:
- A. Charging a battery
- B. Tuning our radio to a favourite station
- C. Switching on a torch
- D. Running a dc motor
Show answer
Answer: B — The text gives the example: 'whenever we tune our radio to a favourite station, we are taking advantage of a special property of ac circuits'.
NCERT Class 12 Physics Ch 7 ("whenever we tune our radio to a favourite station")
In the phasor diagram of a purely resistive ac circuit, the phasors V and I
- A. point in exactly opposite directions
- B. rotate at different angular speeds
- C. point in the same direction at all times
- D. are perpendicular to each other
Show answer
Answer: C — NCERT notes that phasors V and I for the case of a resistor are in the same direction, and this is so for all times.
NCERT Class 12 Physics Ch 7 ("phasors V and I for the case of a resistor are in the same direction")
The peak current in a $10\ \Omega$ resistor is $6$ A. The average power dissipated over one cycle is:
- A. 90 W
- B. 60 W
- C. 180 W
- D. 360 W
Show answer
Answer: C — $P = \tfrac{1}{2} i_m^2 R = 0.5 \times 36 \times 10 = 180$ W.
NCERT Class 12 Physics Ch 7 ("the average power loss P (averaged over a cycle) due to joule heating")
An rms current of $3\ \text{A}$ flows through the $40\ \Omega$ resistor of an ac circuit. The power dissipated is:
- A. $360\ \text{W}$
- B. $720\ \text{W}$
- C. $1080\ \text{W}$
- D. $120\ \text{W}$
Show answer
Answer: A — Power is dissipated only in $R$: $P=I^2R=(3)^2(40)=360\ \text{W}$.
NCERT Class 12 Physics Ch 7 ("maximum power is dissipated in a circuit (through R) at resonance")
A transformer with 100 primary and 200 secondary turns is a:
- A. step-up transformer ($V_s>V_p$)
- B. rectifier
- C. step-down transformer ($V_s<V_p$)
- D. isolation transformer ($V_s=V_p$)
Show answer
Answer: A — With $N_s>N_p$, it is a step-up transformer ($V_s>V_p$).
NCERT Class 12 Physics Ch 7 ("arrangement is called a step-up transformer")
For the same peak voltage, in which case is the peak current through a pure inductor the largest?
- A. largest frequency at fixed inductance
- B. smallest product of frequency and inductance
- C. largest inductance at fixed frequency
- D. largest product of frequency and inductance
Show answer
Answer: B — $i_m=v_m/X_L=v_m/(2\pi f L)$; the current is largest when $2\pi f L$ is smallest, i.e. smallest $f\times L$.
NCERT Class 12 Physics Ch 7 ("XL = wL is called inductive reactance. The current in the inductor lags the voltage by")
A series LCR circuit has $L=0.001\ \text{H}$ and $C=0.001\ \mu\text{F}$. The resonant angular frequency $\omega_0$ is about:
- A. $2000000\ \text{rad/s}$
- B. $1000000000000\ \text{rad/s}$
- C. $1000000\ \text{rad/s}$
- D. $500000\ \text{rad/s}$
Show answer
Answer: C — $\omega_0=\dfrac{1}{\sqrt{LC}}=\dfrac{1}{\sqrt{(0.001)(10^{-9})}}\approx1000000\ \text{rad/s}$.
NCERT Class 12 Physics Ch 7 ("is called the resonant frequency")
An ideal transformer has $N_p=200$ primary turns and $N_s=1000$ secondary turns. If the primary voltage is $110\ \text{V}$, the secondary voltage is:
- A. $22\ \text{V}$
- B. $1100\ \text{V}$
- C. $550\ \text{V}$
- D. $110\ \text{V}$
Show answer
Answer: C — $V_s=\dfrac{N_s}{N_p}V_p=\dfrac{1000}{200}(110)=550\ \text{V}$.
NCERT Class 12 Physics Ch 7 ("the voltage is stepped up (Vs > Vp)")
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