Electromagnetic Induction & AC · JEE Main previous year questions

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.

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.$\mathrm{A}={\mathrm{X}}_{\mathrm{C}},\mathrm{B}=\mathrm{R}$

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 ________ $\text{m}\Omega$.

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, ${\pi }^2=10$ )

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

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 ________ $\mu \text{F}$.

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.$3.14\Omega$

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.

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.$M=\frac{\sqrt{2}{\mu }_0{R}^2}{L}$

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

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

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 :

The equation of current in a purely inductive circuit is $5\sin (49\pi t-30^{\circ })$. If the inductance is $30\text{ mH}$ then the equation for the voltage across the inductor, will be : \{ Let $\pi =\frac{22}{7}$ \}

1. A.$1.47\sin (49\pi t-30^{\circ })$
2. B.$1.47\sin (49\pi t+60^{\circ })$
3. C.$23.1\sin (49\pi t-30^{\circ })$
4. D.$23.1\sin (49\pi t+60^{\circ })$

A transformer operating at primary voltage $8\text{ kV}$ and secondary voltage $160\text{ V}$ serves a load of $80\text{ kW}$. Assuming the transformer to be ideal with purely resistive load and working on unity power factor, the loads in the primary and secondary circuit would be

1. A.$800\Omega$ and $1.06\Omega$
2. B.$10\Omega$ and $500\Omega$
3. C.$800\Omega$ and $0.32\Omega$
4. D.$1.06\Omega$ and $500\Omega$

A series LCR circuit has $\mathrm{L}=0.01\mathrm{H}$, $\mathrm{R}=10\Omega$ and $C=1\mu \mathrm{F}$ and it is connected to ac voltage of amplitude $({\mathrm{V}}_{\mathrm{m}})50\mathrm{V}$. At frequency $60\%$ lower than resonant frequency, the amplitude of current will be approximately :

1. A.$466\mathrm{mA}$
2. B.$312\mathrm{mA}$
3. C.$238\mathrm{mA}$
4. D.$196\mathrm{mA}$

The electric current in a circular coil of 2 turns produces a magnetic induction ${\mathrm{B}}_1$ at its centre. The coil is unwound and is rewound into a circular coil of 5 turns and the same current produces a magnetic induction ${\mathrm{B}}_2$ at its centre. The ratio of $\frac{B_2}{B_1}$ is

1. A.$\frac{5}{2}$
2. B.$\frac{25}{4}$
3. C.$\frac{5}{4}$
4. D.$\frac{25}{2}$

In series RLC resonator, if the self inductance and capacitance become double, the new resonant frequency ($f_2$) and new quality factor ($Q_2$) will be : ($f_1$ = original resonant frequency, $Q_1$ = original quality factor)

1. A.$f_2=\frac{f_1}{2}$ and $Q_2=Q_1$
2. B.$f_2=f_1$ and $Q_2=\frac{Q_1}{Q_2}$
3. C.$f_2=2f_1$ and $Q_2=Q_1$
4. D.$f_2=f_1$ and $Q_2=2Q_1$

1. A.$\frac{1}{L_1}+\frac{1}{L_2}+\frac{1}{M}$
2. B.$L_1+L_2+M$
3. C.$L_1+L_2+2M$
4. D.$L_1+L_2-2M$

Match List-I with List-II. | | List - I | | List - II | | :--- | :--- | :--- | :--- | | (A) | AC generator | (I) | Detects the presence of current in the circuit | | (B) | Galvanometer | (II) | Converts mechanical energy into electrical energy | | (C) | Transformer | (III) | Works on the principle of resonance in AC circuit | | (D) | Metal detector | (IV) | Changes an alternating voltage for smaller or greater value | Choose the correct answer from the options given below :

1. A.(A) - (II), (B) - (I), (C) - (IV), (D) - (III)
2. B.(A) - (II), (B) - (I), (C) - (III), (D) - (IV)
3. C.(A) - (III), (B) - (IV), (C) - (II), (D) - (I)
4. D.(A) - (III), (B) - (I), (C) - (II), (D) - (IV)

If wattless current flows in the AC circuit, then the circuit is :

1. A.Purely Resistive circuit
2. B.Purely Inductive circuit
3. C.LCR series circuit
4. D.RC series circuit only

The current in a coil of self inductance $2.0\text{ H}$ is increasing according to $\mathrm{I}=2\sin (t^2)\text{ A}$. The amount of energy spent during the period when current changes from $0$ to $2\text{ A}$ is $\underline{}\text{ J}$.

A sinusoidal voltage $\mathrm{V}(\mathrm{t})=210\sin 3000\mathrm{t}\mathrm{volt}$ is applied to a series LCR circuit in which $\mathrm{L}=10\mathrm{mH}$, $\mathrm{C}=25\mu \mathrm{F}$ and $\mathrm{R}=100\Omega$. The phase difference $(\Phi )$ between the applied voltage and resultant current will be :

1. A.${\tan }^{-1}(0.17)$
2. B.${\tan }^{-1}(9.46)$
3. C.${\tan }^{-1}(0.30)$
4. D.${\tan }^{-1}(13.33)$

Match List - I with List - II | List-I | List-II | | :--- | :--- | | (a) Magnetic Induction | (i) ${\mathrm{ML}}^2{\mathrm{T}}^{-2}{\mathrm{A}}^{-1}$ | | (b) Magnetic Flux | (ii) ${\mathrm{M}}^0{\mathrm{L}}^{-1}\mathrm{A}$ | | (c) Magnetic Permeability | (iii) ${\mathrm{MT}}^{-2}{\mathrm{A}}^{-1}$ | | (d) Magnetization | (iv) ${\mathrm{MLT}}^{-2}{\mathrm{A}}^{-2}$ | Choose the most appropriate answer from the options given below :

1. A.(a)-(ii), (b)-(iv), (c)-(i), (d)-(iii)
2. B.(a)-(ii), (b)-(i), (c)-(iv), (d)-(iii)
3. C.(a)-(iii), (b)-(ii), (c)-(iv), (d)-(i)
4. D.(a)-(iii), (b)-(i), (c)-(iv), (d)-(ii)

A $100\Omega$ resistance, a $0.1\mu \mathrm{F}$ capacitor and an inductor are connected in series across a 250 V supply at variable frequency. Calculate the value of inductance of inductor at which resonance will occur. Given that the resonant frequency is 60 Hz.

1. A.0.70 H
2. B.70.3 mH
3. C.$7.03\times 10^{-5}$ H
4. D.70.3 H