Power in AC and Power Factor PYQs: JEE Mains Physics

Showing 1–27 of 27 questions

1. 1. 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
2. 2. 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
3. 3. 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
4. 4. 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
5. 5. 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
6. 6. 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
7. 7. 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
8. 8. 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
9. 9. 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
10. 10. 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
11. 11. Given below are two statements: Statement \(I\): An \(AC\) circuit undergoes electrical resonance if it contains either a capacitor or an inductor. Statement \(II\): An \(AC\) circuit containing a pure capacitor or a pure inductor consumes high power due to its non-zero power factor. In the light of above statements, choose the correct answer from the options given below 2023 Medium
12. 12. Given below are two statements: Statement \(I :\) Maximum power is dissipated in a circuit containing an inductor, a capacitor and a resistor connected in series with an \(AC\) source, when resonance occurs Statement \(II :\) Maximum power is dissipated in a circuit containing pure resistor due to zero phase difference between current and voltage. In the light of the above statements, choose the correct answer from the options given below : 2023 Medium
13. 13. Given below are two statements Statement \(I\) : When the frequency of an \(a.c.\) source in a series \(LCR\) circuit increases, the current in the circuit first increases, attains a maximum value and then decreases. Statement \(II:\) In a series \(LCR\) circuit, the value of power factor at resonance is one. In the light of given statements, choose the most appropriate answer from the options given below 2023 Medium
14. 14. In a series \(L R\) circuit with \(X_L=R\). power factor is \(P_1\). If a capacitor of capacitance \(C\) with \(X _{ C }= X _{ L }\) is added to the circuit the power factor becomes \(P _2\). The ratio of \(P_1\) to \(P_2\) will be : 2023 Medium
15. 15. A direct current of \(4\,A\) and an alternating current of peak value \(4\,A\) flow through resistance of \(3\,\Omega\) and \(2\,\Omega\) respectively. The ratio of heat produced in the two resistances in same interval of time will be. 2022 Medium
16. 16. Given below are two statements: statement\(-I\) : The reactance of an ac circuit is zero. It is possible that the circuit contains a capacitor and an inductor. Statement\(-II\) : In \(ac\) circuit, the average power delivered by the source never becomes zero. In the light of the above statements, choose the correct answer from the options given below 2022 Medium
17. 17. To light, a \(50\,W , 100\,V\) lamp is connected, in series with a capacitor of capacitance \(\frac{50}{\pi \sqrt{ x }} \mu F\), with \(200 V , 50 Hz AC\) source. The value of \(x\) will be........ 2022 Hard
18. 18. A series \(LCR\) circuit of \(R=5\, \Omega, L=20\, {mH}\) and \({C}=0.5 \,\mu \,{F}\) is connected across an \({AC}\) supply of \(250\, V\), having variable frequency. The power dissipated at resonance condition is \(.....\,\times 10^{2}\, {W}\) 2021 Medium
19. 19. A sinusoidal voltage of peak value \(250\, V\) is applied to a series \(LCR\) circuit, in which \(R =8 \Omega, L =24\, mH\) and \(C =60 \mu F\). The value of power dissipated at resonant condition is \('x'\, kW\). The value of \(x\) to the nearest integer is ............. 2021 Medium
20. 20. An ac circuit has an inductor and a resistor of resistance \({R}\) in series, such that \({X}_{{L}}=3 {R}\). Now, a capacitor is added in series such that \({X}_{{C}}=2 {R}\). The ratio of new power factor with the old power factor of the circuit is \(\sqrt{5}: {x}\). The value of \({x}\) is ...... . 2021 Medium
21. 21. In a series \(LCR\) circuit, the inductive reactance \(\left( X _{ L }\right)\) is \(10\, \Omega\) and the capacitive reactance \(\left( X _{ C }\right)\) is \(4\, \Omega\). The resistance \(( R )\) in the circuit is \(6\, \Omega\). The power factor of the circuit is : 2021 Medium
22. 22. In an \(LCR\) series circuit, an inductor \(30 \,{mH}\) and a resistor \(1 \, \Omega\) are connected to an \(AC\) source of angular frequency \(300 \, {rad} / {s}\). The value of capacitance for which, the current leads the voltage by \(45^{\circ}\) is \(\frac{1}{x} \times 10^{-3} \, {F}\). Then the value of \(x\) is ..... . 2021 Hard
23. 23. A \(750\, Hz,\) \(20\) \(V\) (rms ) source is connected to a resistance of \(100\, \Omega\) an inductance of \(0.1803\, H\) and a capacitance of \(10\mu ,\) \(F\) all in series. The time in which the resistance (heat capacity \(2 J /{ }^{\circ} C\) ) will get heated by \(10^{\circ} C\). (assume no \(105 s\) of heat to the surroundings) is close to\(.....s\) 2020 Hard
24. 24. In a scries \(LR\) circuit, power of \(400\, W\) is dissipated from a source of \(250\, V , 50\, Hz\). The power factor of the circuit is \(0.8 .\) In order to bring the power factor to unity, a capacitor of value \(C\) is added in series to the \(L\) and \(R\). Taking the value of \(C\) as \(\left(\frac{ n }{3 \pi}\right) \mu F ,\) then value of \(n\) is\(......\) 2020 Medium
25. 25. A series \(AC\) circuit containing an inductor \((20\,mH),\) a capacitor \((120\,\mu F)\) and a resistor \((60\, \Omega )\) is driven by an \(AC\) source of \(24\,V/50\,Hz.\) The energy dissipated in the circuit in \(60\,s\) is 2019 Medium
26. 26. In an \(A.C.\) circuit, the instantaneous \(e.m.f\) and current are given by. \(e=100\) \(sin\) \(20t\) \(i=20sin\) \(\left( {30t - \frac{\pi }{4}} \right)\) In one cycle of \(A.C.\), the average power consumed by the circuit and the wattless current are, respectively 2018 Medium
27. 27. A series \(LR\) circuit is connected to an ac source of frequency \(\omega \) and the inductive reactance is equal to \(2R\). A capacitance of capacitive reactance equal to \(R\) is added in series with \(L\) and \(R\). The ratio of the new power factor to the old one is 2013 Hard

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