Electromagnetic Induction & AC · JEE Main previous year questions

A LCR series circuit driven with $E_{\mathrm{rms}}=90\mathrm{V}$ at frequency $f_d=30\mathrm{Hz}$ has resistance $R=80\Omega$, an inductance with inductive reactance $X_L=20.0\Omega$ and capacitance with capacitive reactance $X_C=80.0\Omega$. The power factor of the circuit is ____.

1. A.0.8
2. B.0.64
3. C.0.9
4. D.0.5

A series LCR circuit with $R=20\Omega$, $L=1.6\mathrm{H}$ and $C=40\mu \mathrm{F}$ is connected to a variable frequency a.c. source. The inductive reactance at resonant frequency is ____ $\Omega$.

1. A.$\frac{9}{2}$
2. B.$\frac{2}{9}$
3. C.$\frac{1}{3}$
4. D.3

A circular current loop of radius $R$ is placed inside square loop of side length $L$ ($L>>R$) such that they are co-planar and their centers coincide. The permeability of free space is ${\mu }_0$. The mutual inductance between circular loop and square loop is ____.

1. A.$2\sqrt{2}\frac{{\mu }_0{L}^2}{R}$
2. B.$\sqrt{2}\frac{{\mu }_0{L}^2}{R}$
3. C.$\sqrt{2}\frac{{\mu }_0{R}^2}{L}$
4. D.$2\sqrt{2}\frac{{\mu }_0{R}^2}{L}$

1. A.4
2. B.8
3. C.6
4. D.10

Match the LIST-I with LIST-II $$\begin{array}{llll}\text{List-I}& & \text{List-II}& \\ \text{A.}& \text{Magnetic induction}& \text{I.}& ML{T}^{-2}{A}^{-2}\\ \text{B.}& \text{Magnetic flux}& \text{II.}& M{L}^2{T}^{-2}{A}^{-2}\\ \text{C.}& \text{Magnetic permeability}& \text{III.}& M{L}^0{T}^{-2}{A}^{-1}\\ \text{D.}& \text{Self inductance}& \text{IV.}& M{L}^2{T}^{-2}{A}^{-1}\end{array}$$ Choose the correct answer from the options given below:

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

An alternating current is represented by the equation, $i=100\sqrt{2}\sin (100\pi t)\text{ampere}$. The RMS value of current and the frequency of the given alternating current are

1. A.$\frac{100}{\sqrt{2}}\mathrm{A},100\mathrm{Hz}$
2. B.$50\sqrt{2}\mathrm{A},50\mathrm{Hz}$
3. C.$100\sqrt{2}\mathrm{A},100\mathrm{Hz}$
4. D.$100\mathrm{A},50\mathrm{Hz}$

An inductor of self inductance $1\mathrm{H}$ is connected in series with a resistor of $100\pi \mathrm{ohm}$ and an ac supply of $100\pi \mathrm{volt}$, $50\mathrm{Hz}$ . Maximum current flowing in the circuit is ____ A.

An electric bulb rated as $100\mathrm{W}-220\mathrm{V}$ is connected to an ac source of rms voltage $220\mathrm{V}$. The peak value of current through the bulb is :

1. A.$0.32\mathrm{A}$
2. B.$0.64\mathrm{A}$
3. C.$0.45\mathrm{A}$
4. D.$2.2\mathrm{A}$

An alternating current is given by $\mathrm{I}={\mathrm{I}}_{\mathrm{A}}\sin \omega t+{\mathrm{I}}_{\mathrm{B}}\cos \omega t$. The r.m.s current will be

1. A.$\frac{\sqrt{{\mathrm{I}}_{\mathrm{A}}^2+{\mathrm{I}}_{\mathrm{B}}^2}}{2}$
2. B.$\sqrt{\frac{{\mathrm{I}}_{\mathrm{A}}^2+{\mathrm{I}}_{\mathrm{B}}^2}{2}}$
3. C.$\frac{|{\mathrm{I}}_{\mathrm{A}}+{\mathrm{I}}_{\mathrm{B}}|}{\sqrt{2}}$
4. D.$\sqrt{{\mathrm{I}}_{\mathrm{A}}^2+{\mathrm{I}}_{\mathrm{B}}^2}$

In a series LCR circuit, a resistor of $300\Omega$, a capacitor of $25\text{ nF}$ and an inductor of $100\text{ mH}$ are used. For maximum current in the circuit, the angular frequency of the ac source is _________ $\times 10^4{\text{ radians s}}^{-1}$

When a coil is connected across a $20\text{ V}$ dc supply, it draws a current of $5\text{ A}$. When it is connected across $20\text{ V}$, $50\text{ Hz}$ ac supply, it draws a current of $4\text{ A}$. The self inductance of the coil is ______ $\text{mH}$. (Take $\pi =3$)

In a coil, the current changes from $-2\mathrm{A}$ to $+2\mathrm{A}$ in $0.2\mathrm{s}$ and induces an emf of $0.1\mathrm{V}$. The self inductance of the coil is :

1. A.$4\mathrm{mH}$
2. B.$2.5\mathrm{mH}$
3. C.$1\mathrm{mH}$
4. D.$5\mathrm{mH}$

For a given series LCR circuit it is found that maximum current is drawn when value of variable capacitance is $2.5\text{ nF}$. If resistance of $200\Omega$ and $100\text{ mH}$ inductor is being used in the given circuit. The frequency of ac source is ________ $\times 10^3\text{ Hz}$ (given ${\pi }^2=10$)

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 ____.

1. A.$10\mathrm{A}$
2. B.$10\mathrm{mA}$
3. C.$68\mathrm{A}$
4. D.$63\mathrm{A}$

The current in an inductor is given by $\mathrm{I}=(3\mathrm{t}+8)$ where $\mathrm{t}$ is in second. The magnitude of induced emf produced in the inductor is $12\mathrm{mV}$. The self-inductance of the inductor ____ $\mathrm{mH}$.

An alternating current at any instant is given by $i=[6+\sqrt{56}\sin (100\pi t+\pi /3)]\mathrm{A}$. The rms value of the current is ____ $\mathrm{A}$.

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

A transformer has an efficiency of $80\%$ and works at $10\text{ V}$ and $4\text{ kW}$. If the secondary voltage is $240\text{ V}$, then the current in the secondary coil is :

1. A.$1.33\text{ A}$
2. B.$13.33\text{ A}$
3. C.$1.59\text{ A}$
4. D.$15.1\text{ A}$

A small square loop of wire of side $l$ is placed inside a large square loop of wire of side $L\left(L=l^2\right)$. The loops are coplanar and their centers coincide. The value of the mutual inductance of the system is $\sqrt{x}\times 10^{-7}\mathrm{H}$, where $x=$ ____.

An AC voltage $V=20\sin 200\pi t$ 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:

1. A.21.6 W
2. B.200 W
3. C.173.2 W
4. D.50 W

1. A.$\frac{\sqrt{2}{\mu }_{0}I}{a}$
2. B.$\frac{{\mu }_{0}I}{\sqrt{2}a}$
3. C.$\frac{{\mu }_{0}I}{2a}$
4. D.$\frac{2{\mu }_{0}I}{a}$

Two coils have mutual inductance $0.002\text{ H}$. The current changes in the first coil according to the relation $i=i_0\sin \omega t$, where $i_0=5\text{ A}$ and $\omega =50\pi \text{ rad/s}$. The maximum value of emf in the second coil is $\frac{\pi }{\alpha }\text{ V}$. The value of $\alpha$ is ________.

A series LCR circuit with $\text{L}=\frac{100}{\pi }\text{ mH}$, $\text{C}=\frac{10^{-3}}{\pi }\text{F}$ and $\text{R}=10\Omega$, is connected across an ac source of $220\text{ V},50\text{ Hz}$ supply. The power factor of the circuit would be _______.