STD 12 -Alternating current PYQs: JEE Mains Physics

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1. 1. A capacitor C is first charged fully with potential difference of \( V_{0} \) and disconnected from the battery. The charged capacitor is connected across an inductor having inductance L. In time t, 25% of the initial energy in the capacitor is transferred to the inductor. The value of t is 2026 Easy
2. 2. 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
3. 3. An a.c. source of angular frequency \(\omega\) is connected across a resistor \(R\) and a capacitor \(C\) in series. The current is observed as \(I\). Now the frequency of the source is changed to \(\omega/4\), (keeping the voltage unchanged) the current is found to be \(I/3\). The ratio of resistance to reactance at frequency \(\omega\) is 2026 Hard
4. 4. An inductor of \(10\) mH, capacitor of \(0.1\ \mu\)F and a resistor of \(100\ \Omega\) are connected in series across an \(a.c\) power supply \(220\) V, \(70\) Hz. The power factor of the given circuit is \(0.5\). The difference in the inductive reactance and capacitance reactance is \(\sqrt{3}\alpha\ \Omega\). The value of \(\alpha\) is _____. 2026 Medium
5. 5. An inductor stores 16 J of magnetic field energy and dissipates 32 W of thermal energy due to its resistance when an a.c. current of 2 A (rms) and frequency 50 Hz flows through it. The ratio of inductive reactance to its resistance is ___________. \((\pi=3.14)\) 2026 Hard
6. 6. For the series LCR circuit connected with 220 V , 50 Hz a.c source as shown in the figure, the power factor is \(\frac{\alpha}{10}\). The value of \(\alpha\) is _________
   2026 Medium
7. 7. The electric current in the circuit is given as \(i=i_{ o }(t / T)\). The r.m.s current for the period \(t=0\) to \(t=T\) is ___________ 2026 Easy
8. 8. The figure given below shows an \(LCR\) series circuit with two switches \(S_1\) and \(S_2\). When switch \(S_1\) is closed keeping \(S_2\) open, the phase difference \((\phi)\) between the current and source voltage is \(30°\) and phase difference is \(60°\) when \(S_2\) is closed keeping \(S_1\) open. The value of \((3L_1 - L_2)\) is _______ H.
   2026 Hard
9. 9. 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
10. 10. A series LCR circuit is connected to an alternating source of emf E. The current amplitude at resonant frequency is \(I_0\). If the value of resistance R becomes twice of its initial value then amplitude of current at resonance will be : 2025 Easy
11. 11. An ac current is represented as
    \(\mathrm{i}=5 \sqrt{2}+10 \cos \left(650 \pi \mathrm{t}+\frac{\pi}{6}\right) \mathrm{Amp}\)
    The r.m.s value of the current is 2025 Easy
12. 12. An alternating current is given by \(\mathrm{I}=\mathrm{I}_{\mathrm{A}} \sin \omega \mathrm{t}+\mathrm{I}_{\mathrm{B}} \cos \omega \mathrm{t}\). The r.m.s current will be ______. 2025 Easy
13. 13. An alternating current is represented by the equation, \(i=100 \sqrt{2} \sin (100 \pi t)\) ampere. The RMS value of current and the frequency of the given alternating current are ________. 2025 Easy
14. 14. An electric bulb rated as \(100 \mathrm{~W}-220 \mathrm{~V}\) is connected to an ac source of rms voltage 220 V. The peak value of current through the bulb is : 2025 Easy
15. 15. An inductor of reactance \(100 \Omega\), a capacitor of reactance \(50 \Omega\), and a resistor of resistance \(50 \Omega\) are connected in series with an AC source of 10 V , 50 Hz. Average power dissipated by the circuit is ________ W. 2025 Easy
16. 16. An inductor of self inductance 1 H connected in series with a resistor of \(100 \pi \mathrm{ohm}\) and an ac supply of \(100 \pi\) volt, 50 Hz. Maximum current flowing in the circuit is ________ A. 2025 Easy
17. 17. For ac circuit shown in figure, \(\mathrm{R}=100 \mathrm{k} \Omega\) and \(\mathrm{C}=100 \mathrm{pF}\) and the phase difference between \(\mathrm{V}_{\text {in }}\) and \(\left(V_B-V_A\right)\) is \(90^{\circ}\). The input signal frequency is \(10^x \mathrm{rad} / \mathrm{sec}\), where ' x ' is ______.
    2025 Hard
18. 18. 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
19. 19. 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
20. 20. A alternating current at any instant is given by \(i=\left[6+\sqrt{56} \sin \left(100 \pi t+\frac{\pi}{3}\right)\right] A\). The rms value of the current is _________ A. 2024 Hard
21. 21. A bulb and a capacitor are connected in series across an AC supply. A dielectric is then placed between the plates of the capacitor. The glow of the bulb: 2024 Hard
22. 22. A capacitor of capacitance \(100\  \mu \mathrm{F}\) is charged to a potential of \(12  \mathrm{~V}\) and connected to a \(6.4 \ \mathrm{mH}\) inductor to produce oscillations. The maximum current in the circuit would be : 2024 Hard
23. 23. A capacitor of reactance \(4 \sqrt{3} \Omega\) and a resistor of resistance \(4 \Omega\) are connected in series with an ac source of peak value \(8 \sqrt{2} \mathrm{~V}\). The power dissipation in the circuit is _______ \(W\). 2024 Hard
24. 24. A coil of negligible resistance is connected in series with \(90 \Omega\) resistor across \(120 \mathrm{~V}, 60 \mathrm{~Hz}\) supply. A voltmeter reads \(36 \mathrm{~V}\) across resistance. Inductance of the coil is _______. 2024 Hard
25. 25. A parallel plate capacitor has a capacitance \(\mathrm{C}=200 \mathrm{pF}\). It is connected to \(230 \mathrm{~V}\) ac supply with an angular frequency \(300 \mathrm{rad} / \mathrm{s}\). The \(\mathrm{rms}\) value of conduction current in the circuit and displacement current in the capacitor respectively are _______. 2024 Hard
26. 26. A series \(L C R\) circuit with \(L=\frac{100}{\pi} \mathrm{mH}, C=\frac{10^{-3}}{\pi} \mathrm{F}\) and \(R=10 \Omega\), is connected across an ac source of \(220 \mathrm{~V}, 50 \mathrm{~Hz}\) supply. The power factor of the circuit would be___________. 2024 Hard
27. 27. A series \(LCR\) circuit is subjected to an AC signal of \(200 \mathrm{~V}, 50 \mathrm{~Hz}\). If the voltage across the inductor \((\mathrm{L}=10 \mathrm{mH})\) is \(31.4 \mathrm{~V}\), then the current in this circuit is _______. 2024 Hard
28. 28. A series \(LR\) circuit connected with an ac source \(E=(25 \sin 1000 t)\  V\) has a power factor of \(\frac{1}{\sqrt{2}}\). If the source of emf is changed to \(E=(20 \sin 2000 t)\ V,\) the new power factor of the circuit will be _______. 2024 Hard
29. 29. \(AC\) alternating emf \(\mathrm{E}=110 \sqrt{2} \sin 100 \mathrm{t}\) volt is applied to a capacitor of \(2 \mu \mathrm{F}\), the rms value of current in the circuit is _______ \(\mathrm{mA}\). 2024 Hard
30. 30. An ac source is connected in given series \(LCR\) circuit. The rms potential difference across the capacitor of \(20 \mu \mathrm{F}\) is _______\(v\). [\(\mathrm{V}=50 \sqrt{2} \sin 100 \mathrm{t}\) volt]
    2024 Hard
31. 31. An AC voltage \(\mathrm{V}=20 \sin 200 \pi t\) is applied to a series \(LCR\) circuit which drives a current \(I=10 \sin \left(200 \pi t+\frac{\pi}{3}\right)\). The average power dissipated is _______. 2024 Hard
32. 32. An alternating voltage \(\mathrm{V}(\mathrm{t})=220 \sin 100 \ \pi \mathrm{t}\) volt is applied to a purely resistive load of \(50\ \Omega\). The time taken for the current to rise from half of the peak value to the peak value is _______. 2024 Hard
33. 33. 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
34. 34. 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
35. 35. In an a.c. circuit, voltage and current are given by: \(V=100 \sin (100 t)\  V\) and \(I=100 \sin \left(100 t+\frac{\pi}{3}\right)\  \mathrm{mA}\) respectively. The average power dissipated in one cycle is _______. 2024 Hard
36. 36. In an ac circuit, the instantaneous current is zero, when the instantaneous voltage is maximum. In this case, the source may be connected to: \(A\). pure inductor. \(B\). pure capacitor. \(C\). pure resistor. \(D\). combination of an inductor and capacitor. Choose the correct answer from the options given below: 2024 Hard
37. 37. \(LCR\) 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
38. 38. Match List I with List \(II\) Choose the correct answer from the options given below:
    2024 Hard
39. 39. When a coil is connected across a \(20 \mathrm{~V}\) DC supply, it draws a current of \(5 \mathrm{~A}\). When it is connected across \(20 \mathrm{~V}, 50 \mathrm{~Hz}\) AC supply, it draws a current of \(4 \mathrm{~A}\). The self inductance of the coil is _______ \(\mathrm{mH}\). (Take \(\pi=3\) ) 2024 Hard
40. 40. When a dc voltage of \(100 \mathrm{~V}\) is applied to an inductor, a dc current of \(5 \mathrm{~A}\) flows through \(1\) . When an ac voltage of \(200 \mathrm{~V}\) peak value is connected to inductor, its inductive reactance is found to be \(20 \sqrt{3} \Omega\). The power dissipated in the circuit is _______\(W\). 2024 Hard
41. 41. A capacitor of capacitance \(150.0\,\mu F\) is connected to an alternating source of \(emf\) given by \(E =36\) \(\sin (120 \pi t ) V\). The maximum value of current in the circuit is approximately equal to \(......\,A\) 2023 Medium
42. 42. 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
43. 43. A series \(LCR\) circuit consists of \(R =80\,\Omega X _{ L }=100\, \Omega\) and \(X _{ C }=40\, \Omega\) The input voltage is \(2500 \cos (100 \pi t )\,V\). The amplitude of current, in the circuit, is \(................A.\) 2023 Medium
44. 44. 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
45. 45. 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
46. 46. An alternating voltage source \(V =260 \sin (628\,t )\) is connected across a pure inductor of \(5\,mH\). Inductive reactance in the circuit is \(......... \Omega\) 2023 Easy
47. 47. An inductor of \(0.5\,mH\), a capacitor of \(20\,\mu\,F\) and resistance of \(20\,\Omega\) 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 - 2023 Medium
48. 48. An inductor of inductance \(2\,\mu\,H\) 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 is \(\frac{1}{x} F\), where the value of \(x\) is \(.........\). \(\left(\right.\) Take \(\left.\pi=\frac{22}{7}\right)\) 2023 Easy
49. 49. An \(LCR\) series circuit of capacitance \(62.5\,nF\) and resistance of \(50\,\Omega\). 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 \(\left.\pi^2=10\right)\) 2023 Easy
50. 50. An oscillating \(LC\) circuit consists of a \(75\,mH\) inductor and a \(1.2\,\mu F\) capacitor. If the maximum charge to the capacitor is \(2.7\,\mu C\). The maximum current in the circuit will be \(...........\,mA\). 2023 Medium

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