JEE Main Alternating Current PYQ

11. (JEE Main 2023 (Online) 31st January Morning Shift)

An inductor of $0.5 mH$ , a capacitor of $20 μ F$ and resistance of $20 Ω$ are connected in series with a $220 V$ ac source. If the current is in phase with the emf, the amplitude of current of the circuit is $\sqrt{x}$ A. The value of $x$ is ___________

Correct Answer is (242)

$X_{L} = X_{C}$

So, $Z = R = 20 Ω$

$\begin{aligned} i_{rms} = \frac{220}{20} = 11 \\ i_{max} = 11 \sqrt{2} = \sqrt{242} \end{aligned}$

12. (JEE Main 2023 (Online) 29th January Evening Shift)

An inductor of inductance 2 $μ H$ is connected in series with a resistance, a variable capacitor and an AC source of frequency 7 kHz. The value of capacitance for which maximum current is drawn into the circuit $\frac{1}{x} F$ , where the value of $x$ is ___________.

(Take $π = \frac{22}{7}$ )

Correct Answer is (3872)

>Current drawn is maximum when circuit is in resonance.

$ω = \frac{1}{\sqrt{L C}}$

$2 π (7000) = \frac{1}{\sqrt{2 \times 10^{- 6} C}}$

$\Rightarrow C = \frac{1}{3872} F$

13. (JEE Main 2023 (Online) 25th January Morning Shift)

An LCR series circuit of capacitance 62.5 nF and resistance of 50 $Ω$ , is connected to an A.C. source of frequency 2.0 kHz. For maximum value of amplitude of current in circuit, the value of inductance is __________ mH.

(Take $π^{2} = 10$ )

Correct Answer is (100)

$∵$ For maximum amplitude of current, circuit should be at resonance.

$\begin{aligned} ∴ X_{L} = X_{C} \\ ω L = \frac{1}{ω C} \\ L = \frac{1}{ω^{2} C} \\ = \frac{1}{{(2 π \times 2 \times 10^{3})}^{2} \times 62.5 \times 10^{- 9}} \\ = 100 mH \end{aligned}$

14. (JEE Main 2023 (Online) 24th January Morning Shift)

In the circuit shown in the figure, the ratio of the quality factor and the band width is ___________ s.

JEE Main 2023 (Online) 24th January Morning Shift Physics - Alternating Current Question 11 English

Correct Answer is (10)

Bandwidth $Δ ω = \frac{R}{L}$

Quality factor $Q = \frac{1}{R} \sqrt{\frac{L}{C}}$

So $\frac{Q}{Δ ω} = \frac{\frac{1}{R} \sqrt{\frac{L}{C}}}{\frac{R}{L}}$

$\begin{aligned} = \frac{L^{\frac{3}{2}}}{R^{2} \sqrt{C}} \\ = \frac{3^{\frac{3}{2}}}{10^{2} {(27 \times 10^{- 6})}^{\frac{1}{2}}} \\ = \frac{3 \sqrt{3}}{100 (3 \sqrt{3} \times 10^{- 3})} \\ = 10 \end{aligned}$

15. (JEE Main 2022 (Online) 25th July Evening Shift)

When you walk through a metal detector carrying a metal object in your pocket, it raises an alarm. This phenomenon works on

A. Electromagnetic induction

B. Resonance in ac circuits

C. Mutual induction in ac circuits

D. Interference of electromagnetic waves

Correct Option is (B)

Metal detector works on the principle of resonance in ac circuits.