Half Power Frequency, Quality Factor, Resonance in AC Circuit PYQs: JEE Mains Physics

Showing 1–28 of 28 questions

1. 1. A series LCR circuit with \(R = 20\ \Omega\), \(L = 1.6\text{ H}\) and \(C = 40\ \mu\text{F}\) is connected to a variable frequency a.c. source. The inductive reactance at resonant frequency is _______ \(\Omega\). 2026 Easy
2. 2. Using a variable-frequency a.c. voltage source, the maximum current measured in the given LCR circuit is 50 mA for \(V =5 \sin (100 t )\). The values of L and \(R\) are shown in the figure. The capacitance of the capacitor \(( C )\) used is ___________ \(\mu F\).
   2026 Hard
3. 3. Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).
   Assertion (A) : Choke coil is simply a coil having a large inductance but a small resistance. Choke coils are used with fluorescent mercury-tube fittings. If household electric power is directly connected to a mercury tube, the tube will be damaged.
   Reason (R): By using the choke coil, the voltage across the tube is reduced by a factor \(\left(R / \sqrt{R^2+\omega^2 L^2}\right)\), where \(\omega\) is frequency of the supply across resistor \(R\) and inductor L . If the choke coil were not used, the voltage across the resistor would be the same as the applied voltage.
   In the light of the above statements, choose the most appropriate answer from the options given below : 2025 Medium
4. 4. In a series LCR circuit, a resistor of \(300 \Omega\), a capacitor of 25 nF and an inductor of 100 mH are used. For maximum current in the circuit, the angular frequency of the ac source is _____ \(\times 10^4\) radians \(\mathrm{s}^{-1}\). 2025 Medium
5. 5. For a given series \(LCR\) circuit it is found that maximum current is drawn when value of variable capacitance is \(2.5 \mathrm{nF}\). If resistance of \(200 \Omega\) and \(100 \mathrm{mH}\) inductor is being used in the given circuit. The frequency of ac source is _______ \(\times 10^3 \mathrm{~Hz}\). (given \(\pi^2=10\) ) 2024 Hard
6. 6. Given below are two statements : Statement \(I\) : In an \(LCR\) series circuit, current is maximum at resonance. Statement \(II\) : Current in a purely resistive circuit can never be less than that in a series LCR circuit when connected to same voltage source. In the light of the above statements, choose the correct from the options given below : 2024 Hard
7. 7. \(LCR\) circuit is at resonance for a capacitor \(C\), inductance \(L\) and resistance \(R\). Now the value of resistance is halved keeping all other parameters same. The current amplitude at resonance will be now what? 2024 Hard
8. 8. A series combination of resistor of resistance \(100\,\Omega\), inductor of inductance \(1\,H\) and capacitor of capacitance \(6.25\,\mu F\) is connected to an ac source. The quality factor of the circuit will be \(.............\). 2023 Medium
9. 9. A series \(LCR\) circuit is connected to an \(AC\) source of \(220\,V , 50\,Hz\). The circuit contains a resistance \(R =80\,\Omega\), an inductor of inductive reactance \(X _{ L }=70\,\Omega\), and a capacitor of capacitive reactance \(X _{ C }=130\,\Omega\). The power factor of circuit is \(\frac{ X }{10}\). The value of \(x\) is: 2023 Medium
10. 10. A series \(LCR\) circuit is connected to an ac source of \(220\,V , 50 Hz\). The circuit contain a resistance \(R=100 \Omega\) and an inductor of inductive reactance \(X_L=79.6 \Omega\). The capacitance of the capacitor needed to maximize the average rate at which energy is supplied will be \(..........\mu F\). 2023 Medium
11. 11. As per the given graph choose the correct representation for curve \(A\) and curve \(B\).Where \(X _{ C }=\) reactance of pure capacitive circuit connected with \(A.C.\) source \(X _{ L }=\) reactance of pure inductive circuit connected with \(A.C.\) source \(R =\) impedance of pure resistive circuit connected with \(A.C.\) source \(Z =\) Impedance of the LCR series circuit \(\}\)
    2023 Medium
12. 12. In the circuit shown in the figure, the ratio of the quality factor and the band width is \(.............\) s.
    2023 Medium
13. 13. Match the List\(-I\) with List\(-II\).

    List \(I\)	List \(II\)
    \(A\) \(AC\) generator	\(I\) Presence of both \(L\) and \(C\)
    \(B\) Transformer	\(II\) Electromagnetic Induction
    \(C\)Resonance phenomenon to occur	\(III\) Quality factor
    \(D\)Sharpness of resonance	\(IV\) Mutual Inductance

    Choose the correct answer from the options given below: 2023 Medium
14. 14. A series \(L C R\) circuit has \(L=0.01\,H, R=10\,\Omega\) and \(C =1\,\mu F\) and it is connected to ac voltage of amplitude \(\left( V _{ m }\right) 50\,V\). At frequency \(60 \%\) lower than resonant frequency, the amplitude of current will be approximately \(...............\,mA\) 2022 Hard
15. 15. For a series \(LCR\) circuit, \(I\) vs \(\omega\) curve is shown \((A)\) To the left of \(\omega_{r}\), the circuit is mainly capacitive. \((B)\) To the left of \(\omega_{r}\), the circuit is mainly inductive. \((C)\) At \(\omega_{r}\), impedance of the circuit is equal to the resistance of the circuit. \((D)\) At \(\omega_{t}\), impedance of the circuit is \(0\). Choose the most appropriate answer from the options given below
    2022 Hard
16. 16. The frequencies at which the current amplitude in an \(LCR\) series circuit becomes \(\frac{1}{\sqrt{2}}\) times its maximum value, are \(212\,rad\,s ^{-1}\) and \(232\,rad\,s ^{-1}\). The value of resistance in the circuit is \(R =5 \Omega\). The self inductance in the circuit is \(.........mH\) 2022 Medium
17. 17. To increase the resonant frequency in series \(LCR\) circuit, 2022 Medium
18. 18. When you walk through a metal detector carrying a metal object in your pocket, it raises an alarm. This phenomenon works on 2022 Medium
19. 19. A \(100 \,\Omega\) resistance, a \(0.1\, \mu {F}\) capacitor and an inductor are connected in series across a \(250 \,{V}\) supply at variable frequeny. Calculate the value of inductance of inductor at which resonance will occur. Given that the resonant frequency is \(60\, {Hz}\). (In \({H}\)) 2021 Medium
20. 20. A resonance circuit having inductance and resistance \(2 \times 10^{-4} H\) and \(6.28 \Omega\) respectively oscillates at \(10\, MHz\) frequency. The value of quality factor of this resonator is ......... \([\pi=3.14]\) 2021 Medium
21. 21. A transmitting station releases waves of wavelength \(960\, m\). A capacitor of \(2.56\, \mu F\) is used in the resonant circuit. The self inductance of coil necessary for resonance is ............. \(-\times 10^{-8} H\) 2021 Medium
22. 22. Find the peak current and resonant frequency of the following circuit (as shown in figure).
    2021 Hard
23. 23. In a scries \(LCR\) resonance circuit, if we change the resistance only, from a lower to higher value 2021 Medium
24. 24. In a series \(LCR\) resonant circuit, the quality factor is measured as \(100\) If the inductance is increased by two fold and resistance is decreased by two fold, then the quality factor after this change will be ......... 2021 Hard
25. 25. An \(AC\) circuit has \(R =100 \Omega, C =2\, \mu F\) and \(L =80\, mH ,\) connected in series. The quality factor of the circuit is\(.......\) 2020 Medium
26. 26. For an \(RLC\) circuit driven with voltage of amplitude \(v_m\) and frequency \({\omega _0} = \frac{1}{{\sqrt {LC} }}\) the current exhibits resonance. The quality factor, \(Q\) is given by: 2018 Easy
27. 27. The plot given below is of the average power delivered to an \(LRC\) circuit versus frequency. The quality factor of the circuit is
    2013 Medium
28. 28. When resonance is produced in a series \(LCR\) circuit, then which of the following is not correct ? 2013 Medium

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