Electromagnetic Induction & AC · JEE Main previous year questions

2023 12 questions

1. Q462023 · 12 Apr 2023 · Shift 1

   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.

   1. A.Both Statement I and Statement II are False.
   2. B.Statement I is incorrect but Statement II is true.
   3. C.Both Statement I and Statement II are true.
   4. D.Statement I is correct but Statement II is false.
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   Answer: C

2. Q472023 · 11 Apr 2023 · Shift 1
   
   1. A.$\mathrm{A}={\mathrm{X}}_{\mathrm{L}},\mathrm{B}=\mathrm{R}$
   2. B.$\mathrm{A}={\mathrm{X}}_{\mathrm{L}},\mathrm{B}=\mathrm{Z}$
   3. C.$\mathrm{A}={\mathrm{X}}_{\mathrm{C}},\mathrm{B}={\mathrm{X}}_{\mathrm{L}}$
   4. D.$\mathrm{A}={\mathrm{X}}_{\mathrm{C}},\mathrm{B}=\mathrm{R}$
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   Answer: C

3. Q592023 · 6 Apr 2023 · Shift 1· Numerical answer

   An ideal transformer with purely resistive load operates at $12\text{ kV}$ on the primary side. It supplies electrical energy to a number of nearby houses at $120\text{ V}$. The average rate of energy consumption in the houses served by the transformer is $60\text{ kW}$. The value of resistive load (${\text{R}}_S$) required in the secondary circuit will be ________ $\text{m}\Omega$.

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   Answer: 240

4. Q522023 · 6 Apr 2023 · Shift 2· Numerical answer

   Two concentric circular coils with radii $1\text{ cm}$ and $1000\text{ cm}$, and number of turns $10$ and $200$ respectively are placed coaxially with centers coinciding. The mutual inductance of this arrangement will be ___________ $\times 10^{-8}\text{H}$. (Take, ${\pi }^2=10$ )

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   Answer: 4

5. Q332023 · 1 Feb 2023 · Shift 1

   Match 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 Induction | Choose the correct answer from the options given below :

   1. A.A-II, B-I, C-III, D-IV
   2. B.A-IV, B-III, C-I, D-II
   3. C.A-II, B-IV, C-I, D-III
   4. D.A-IV, B-II, C-I, D-III
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   Answer: C

6. Q562023 · 1 Feb 2023 · Shift 1· Numerical answer

   A series LCR circuit is connected to an ac source of $220\text{ V},50\text{ Hz}$. The circuit contain a resistance $\text{R}=100\Omega$ and an inductor of inductive reactance ${\text{X}}_L=79.6\Omega$. The capacitance of the capacitor needed to maximize the average rate at which energy is supplied will be ________ $\mu \text{F}$.

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   Answer: 40

7. Q462023 · 31 Jan 2023 · Shift 2

   An alternating voltage source $\mathrm{V}=260\sin (628t)$ is connected across a pure inductor of $5\text{ mH}$. Inductive reactance in the circuit is :

   1. A.$6.28\Omega$
   2. B.$0.318\Omega$
   3. C.$0.5\Omega$
   4. D.$3.14\Omega$
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   Answer: D

8. Q522023 · 31 Jan 2023 · Shift 2· Numerical answer

   A series LCR circuit consists of $\mathrm{R}=80\Omega$, ${\mathrm{X}}_L=100\Omega$, and ${\mathrm{X}}_C=40\Omega$. The input voltage is $2500\cos (100\pi t)\text{V}$. The amplitude of current, in the circuit, is ___________ A.

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   Answer: 25

9. Q322023 · 29 Jan 2023 · Shift 1

   Find the mutual inductance in the arrangement, when a small circular loop of wire of radius '$R$' is placed inside a large square loop of wire of side $L(L\gg R)$. The loops are coplanar and their centres coincide :

   1. A.$M=\frac{\sqrt{2}{\mu }_{0}R}{L^2}$
   2. B.$M=\frac{2\sqrt{2}{\mu }_{0}R}{L^2}$
   3. C.$M=\frac{2\sqrt{2}{\mu }_0{R}^2}{L}$
   4. D.$M=\frac{\sqrt{2}{\mu }_0{R}^2}{L}$
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   Answer: C

10. Q362023 · 29 Jan 2023 · Shift 1
    
    1. A.$\frac{{\mu }_{0}I}{\pi a}$
    2. B.$\frac{{\mu }_{0}I}{4\pi a}$
    3. C.$\frac{{\mu }_{0}I}{2\pi a}$
    4. D.0
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    Answer: A

11. Q432023 · 29 Jan 2023 · Shift 2

    The electric current in a circular coil of four turns produces a magnetic induction 32 T at its centre. The coil is unwound and is rewound into a circular coil of single turn, the magnetic induction at the centre of the coil by the same current will be :

    1. A.2 T
    2. B.4 T
    3. C.8 T
    4. D.16 T
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    Answer: A

12. Q552023 · 25 Jan 2023 · Shift 2· Numerical answer

    A series LCR circuit is connected to an AC source of 220 V, 50 Hz. The circuit contains a resistance $\mathrm{R}=80\Omega$, an inductor of inductive reactance ${\mathrm{X}}_{\mathrm{L}}=70\Omega$, and a capacitor of capacitive reactance ${\mathrm{X}}_{\mathrm{C}}=130\Omega$. The power factor of circuit is $\frac{x}{10}$. The value of $x$ is :

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    Answer: 8