JEE Main 2021 — Electromagnetism

A coil is placed in a magnetic field $\vec{B}$ as shown below :  A current is induced in the coil because $\vec{B}$ is :

If $2.5\times {10}^{-6}N$ average force is exerted by a light wave on a non-reflecting surface of $30{\mathrm{cm}}^{2}$ area during $40\mathrm{min}$ of time span, the energy flux of light just before it falls on the surface is _______ $W{\mathrm{cm}}^{-2}.$(Round off to the Nearest Integer), (Assume complete absorption and normal incidence conditions are there)

A long solenoid with $1000\mathrm{turns}{m}^{-1}$ has a core material with relative permeability $500$ and volume ${10}^{3}{\mathrm{cm}}^{3}.$ If the core material is replaced by another material having relative permeability of $750$ with same volume maintaining same current of $0.75A$ in the solenoid, the fractional change in the magnetic moment of the core would be approximately $(\frac{x}{499}).$ Find the value of $x.$

The temperature of $3.00\mathrm{mol}$ of an ideal diatomic gas is increased by $40.0^{\circ}C$ without changing the pressure of the gas. The molecules in the gas rotate but do not oscillate. If the ratio of change in internal energy of the gas to the amount of workdone by the gas is $\frac{x}{10}.$ Then the value of $x$ (round off to the nearest integer) is $_________.$ $($ Given$R=8.31J{\mathrm{mol}}^{-1}{K}^{-1})$

The fractional change in the magnetic field intensity at a distance $r$ from centre on the axis of current carrying coil of radius $a$ to the magnetic field intensity at the centre of the same coil is: (Take $r<a$)

Two ions of masses $4\mathrm{amu}$ and $16\mathrm{amu}$ have charges $+2e$ and $+3e$ respectively. These ions pass through the region of the constant perpendicular magnetic field. The kinetic energy of both ions is the same. Then:

A proton and an $\alpha$-particle, having kinetic energies ${K}_{p}$ and ${K}_{\alpha }$, respectively, enter into a magnetic field at right angles. The ratio of the radii of the trajectory of proton to that of $\alpha$ -particle is $2:1$. The ratio of ${K}_{p}:{K}_{\alpha }$ is:

A loop of flexible wire of irregular shape carrying current is placed in an external magnetic field. Identify the effect of the field on the wire.

A hairpin like shape as shown in figure is made by bending a long current carrying wire. What is the magnitude of a magnetic field at point $P$ which lies on the centre of the semicircle ? 

A charge $Q$ is moving $d\vec{l}$ distance in the magnetic field $\vec{B}$. Find the value of work done by $\vec{B}$.

In an LCR series circuit, the power factor is unity. What is the phase difference between current and voltage?

For the given circuit the current $i$ through the battery when the key in closed and the steady state has been reached is 

A bar magnet is passing through a conducting loop of radius $R$ with velocity $v.$ The radius of the bar magnet is such that it just passes through the loop. The induced e.m.f. in the loop can be represented by the approximate curve:  

In the given figure the magnetic flux through the loop increases according to the relation ${\phi }_{B}(t)=10{t}^{2}+20t$, where ${\phi }_{B}$ is in milliwebers and $t$ is in seconds. The magnitude of current through $R=2\Omega$ resistor at $t=5s$ is _____ $\mathrm{mA}.$ 

The arm $PQ$ of a rectangular conductor is moving from $x=0$ to $x=2b$ outwards and then inwards from $x=2b$ to $x=0$ as shown in the figure. A uniform magnetic field perpendicular to the plane is acting from $x=0$ to $x=b.$ Identify the graph showing the variation of different quantities with distance:  

A circular conducting coil of radius $1m$ is being heated by the change of magnetic field $\vec{B}$ passing perpendicular to the plane in which the coil is laid. The resistance of the coil is $2\mu \Omega$. The magnetic field is slowly switched off such that its magnitude changes in time as $B=\frac{4}{\pi }\times {10}^{-3}T(1-\frac{t}{100})$ The energy dissipated by the coil before the magnetic field is switched off completely is $E=______\mathrm{mJ}$.

A coil of inductance $2H$ having negligible resistance is connected to a source of supply whose voltage is given by $V=3t$ volt. (where $t$ is in second). If the voltage is applied when $t=0$, then the energy stored in the coil after $4s$ in $J$,

An $AC$ source rated $220V,50\mathrm{Hz}$ is connected to a resistor. The time taken by the current to change from its maximum to the rms value is :

An AC circuit has an inductor and a resistor of resistance $R$ in series, such that ${X}_{L}=3R$. Now, a capacitor is added in series such that ${X}_{C}=2R$. the ratio of the new power factor with the old power factor of the circuit is $\sqrt{5}:x$. The value of $x$ is

A series LCR circuit driven by $300V$ at a frequency of $50\mathrm{Hz}$ contains a resistance $R=3k\Omega$, an inductor of inductive reactance ${X}_{L}=250\pi \Omega$ and an unknown capacitor. The value of capacitance to maximise the average power should be: $(\text{take}{\pi }^{2}=10)$

An inductor of $10\mathrm{mH}$ is connected to a $20V$ battery through a resistor of $10k\Omega$ and a switch. After a long time, when maximum current is set up in the circuit, the current is switched off. The current in the circuit after $1\mu s$ is $\frac{x}{100}\mathrm{mA}$. Then $x$ is equal to ______ . (Take ${e}^{-1}=0.37$)

Two circuits are shown in figure $(a)$ and $(b)$. At a frequency of _______ $\mathrm{rad}{s}^{-1}$ the average power dissipated in one cycle will be the same in both the circuits. 

For a series $\mathrm{LCR}$ circuit with $R=100\Omega ,L=0.5\mathrm{mH}$ and $C=0.1\mathrm{pF}$ connected across $220V-50\mathrm{Hz}$ $\mathrm{AC}$ supply, the phase angle between current and supplied voltage and the nature of the circuit is:

In a series LCR circuit, the inductive reactance $({X}_{L})$ is $10\Omega$ and the capacitive reactance $({X}_{C})$ is $4\Omega$. The resistance $(R)$ in the circuit is $6\Omega$. The power factor of the circuit is :

In an $LCR$ series circuit, an inductor $30\mathrm{mH}$ and a resistor $1\Omega$ are connected to an $\mathrm{AC}$ source of angular frequency $300\mathrm{rad}{s}^{-1}.$ 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

The time taken for the magnetic energy to reach $25%$ of its maximum value, when a solenoid of resistance $R$, inductance $L$ is connected to a battery, is :

Match List-I with List-II <table class="pyq-table"><tbody><tr><td></td><td>List-i</td><td></td><td>List-II</td></tr><tr><td>a</td><td>Phase difference between current and voltage in a purely resistive AC circuit</td><td>i</td><td>$\frac{\pi }{2};$ current leads voltage</td></tr><tr><td>b</td><td>Phase difference between current and voltage in a pure inductive AC circuit</td><td>ii</td><td>zero</td></tr><tr><td>c</td><td>Phase difference between current and voltage in a pure capacitive AC circuit</td><td>iii</td><td>$\frac{\pi }{2};$ current lags voltage</td></tr><tr><td>d</td><td>Phase difference between current and voltage in an LCR series circuit</td><td>iv</td><td>${\mathrm{tan}}^{-1}(\frac{{X}_{C}-{X}_{L}}{R})$</td></tr></tbody></table>Choose the most appropriate answer from the options given below :

An $RC$ circuit as shown in the figure is driven by a $AC$ source generating a square wave. The output wave pattern monitored by $CRO$ would look close to : 

A sinusoidal voltage of peak value $250V$ is applied to a series $LCR$ circuit, in which $R=8\Omega ,L=24\mathrm{mH}$ and $C=60\mu F$. The value of power dissipated at resonant condition is $x$ $\mathrm{kW}$. The value of $x$ to the nearest integer is _______.

In a series LCR resonant circuit, the quality factor is measured as $100$. If the inductance is increased by two fold and resistance is decreased by two fold, then the quality factor after this change will be _______

A series LCR circuit is designed to resonate at an angular frequency ${\omega }_{0}={10}^{5}\mathrm{rad}{s}^{-1}.$ The circuit draws $16W$ power from $120V$ source at resonance. The value of resistance $R$ in the circuit is ________ $\Omega .$

Two wires of same length and thickness having specific resistances $6\Omega \mathrm{cm}$ and $3\Omega \mathrm{cm}$ respectively are connected in parallel. The effective resistivity is $\rho \Omega cm$. The value of $\rho$ to the nearest integer, is ___ .

A coil having $N$ turns is wound tightly in the form of a spiral with inner and outer radii $a$ and $b$ respectively. Find the magnetic field at centre, when a current $I$ passes through coil :

The electric field in a plane electromagnetic wave is given by, $E=50\mathrm{sin}(500x-10\times {10}^{10}t)V{m}^{-1}$. The velocity of an electromagnetic wave in this medium is: (Given $c=$ the speed of light in vacuum).

The electric field in an electromagnetic wave is given by $E=(50N{C}^{-1})\mathrm{sin}\omega (t-\frac{x}{c})$ The energy contained in a cylinder of volume $V$ is $5.5\times {10}^{-12}J.$ The value of $V$ is _______ ${\mathrm{cm}}^{3}.$ (given ${\epsilon }_{0}=8.8\times {10}^{-12}{C}^{2}{N}^{-1}{m}^{-2}$)

The electric field in a plane electromagnetic wave is given by $\vec{E}=200\mathrm{cos}[(0.5\times {10}^{3}{m}^{-1})x-(1.5\times {10}^{11}\mathrm{rad}{s}^{-1})t]V{m}^{-1}\hat{j}$. If this wave falls normally on a perfectly reflecting surface having an area of $100{\mathrm{cm}}^{2}$. If the radiation pressure exerted by the E.M. wave on the surface during a $10\mathrm{min}$ exposure is $\frac{k}{{10}^{9}}N{m}^{-2}$. Find the value of $k$

A linearly polarised electromagnetic wave in vacuum is $E=3.1\mathrm{cos}[(1.8)z-(5.4\times {10}^{6})t]\hat{i}N{C}^{-1}$ is incident normally on a perfectly reflecting wall at $z=a$. Choose the correct option.

A light beam is described by $E=800\mathrm{sin}\omega (t-\frac{x}{c}).$ An electron is allowed to move normal to the propagation of light beam with a speed of $3\times {10}^{7}{ms}^{-1}$. What is the maximum magnetic force exerted on the electron?

A plane electromagnetic wave propagating along y-direction can have the following pair of electric field $(\vec{E})$ and magnetic field $(\vec{B})$ components.

Red light differs from blue light as they have :

A radiation is emitted by $1000W$ bulb and it generates an electric field and magnetic field at $P$, placed at a distance of $2m$. The efficiency of the bulb is $1.25%$. The value of peak electric field at $P$ is $x\times {10}^{-1}V{m}^{-1}$. Value of $x$ is (Rounded-off to the nearest integer) [Take ${\epsilon }_{0}=8.85\times {10}^{-12}{C}^{2}{N}^{-1}{m}^{-2},c=3\times {10}^{6}m{s}^{-1}$]

For an electromagnetic wave travelling in free space, the relation between average energy densities due to electric $({U}_{e})$ and magnetic $({U}_{m})$ fields is :

Match List - I with List - II.<table class="pyq-table"><tbody><tr><td colspan="2" rowspan="1">List-I</td><td colspan="2" rowspan="1">List-II</td></tr><tr><td>(a)</td><td>Source of microwave frequency</td><td>(i)</td><td>Radioactive decay of nucleus</td></tr><tr><td>(b)</td><td>Source of infrared frequency</td><td>(ii)</td><td>Magnetron</td></tr><tr><td>(c)</td><td>Source of Gamma Rays</td><td>(iii)</td><td>Inner shell electrons</td></tr><tr><td>(d)</td><td>Source of $X$-rays</td><td>(iv)</td><td>Vibration of atoms and molecules</td></tr><tr><td></td><td></td><td>(v)</td><td>LASER</td></tr><tr><td></td><td></td><td>(vi)</td><td>RC circuit</td></tr></tbody></table>Choose the correct answer from the options given below:

A parallel plate capacitor has plate area A and separation d. It is charged to potential V. The energy stored in the capacitor is:

A deuteron and an alpha particle having equal kinetic energy enter perpendicular into a magnetic field. Let ${r}_{d}$ and ${r}_{\alpha }$ be their respective radii of circular path. The value of $\frac{{r}_{d}}{{r}_{\alpha }}$ is equal to:

A plane electromagnetic wave of frequency $100\mathrm{MHz}$ is traveling in a vacuum along the $x-$direction. At a particular point in space and time, $\vec{B}=2.0\times {10}^{-8}\hat{k}T\cdot$ (where, $\hat{k}$ is unit vector along $z-$direction) What is $\vec{E}$ at this point?

A $10\Omega$ resistance is connected across $220V-50\mathrm{Hz}$ AC supply. The time taken by the current to change from its maximum value to the $\mathrm{rms}$ value is:

A proton, a deuteron and an $\alpha$ particle are moving with same momentum in a uniform magnetic field. The ratio of magnetic forces acting on them ______ is and their speed is ______ in the ratio.

A small square loop of side $a$ and one turn is placed inside a larger square loop of side $b$ and one turn $(b\gg a).$ The two loops are coplanar with their centres coinciding. If a current $I$ is passed in the square loop of side $b,$ then the coefficient of mutual inductance between the two loops is :

Consider an electrical circuit containing a two way switch $S.$ Initially $S$ is open and then ${T}_{1}$ is connected to ${T}_{2}.$ As the current in $R=6\Omega$ attains a maximum value of steady-state level, ${T}_{1}$ is disconnected from ${T}_{2}$ and immediately connected to ${T}_{3}.$ Potential drop across $r=3\Omega$ resistor immediately after ${T}_{1}$ is connected to ${T}_{3}$ is $______V.$ (Round off to the Nearest Integer) 

The magnetic field vector of an electromagnetic wave is given by $B={B}_{0}\frac{\hat{i}+\hat{j}}{\sqrt{2}}\mathrm{cos}(kz-\omega t)$ where $\hat{i},\hat{j}$ represents unit vector along $x$ and $y$-axis respectively. At $t=0s,$ two electric charges ${q}_{1}$ of $4\pi$ coulomb and ${q}_{2}$ of $2\pi$ coulomb located at $(0,0,\frac{\pi }{k})$ and $(0,0,\frac{3\pi }{k}),$ respectively, have the same velocity of $0.5c\hat{i},$ (where $c$ is the velocity of light ). The ratio of the force acting on charge ${q}_{1}$ to ${q}_{2}$ is :

Figure $A$ and $B$ shown two long straight wires of circular cross-section ( $a$ and $b$ with $a<b$ ), carrying current $I$ which is uniformly distributed across the cross-section. The magnitude of magnetic field $B$ varies with radius $r$ and can be represented as: 

A solenoid of $1000$ turns per metre has a core with relative permeability $500.$ Insulated windings of the solenoid carry an electric current of $5A.$ The magnetic flux density produced by the solenoid is: (Permeability of free space$=4\pi \times {10}^{-7}H{m}^{-1}$)

A particle of mass $1\mathrm{mg}$ and charge $q$ is lying at the mid-point of two stationary particles kept at a distance $2m$ when each is carrying same charge $q$. If the free charged particle is displaced from its equilibrium position through distance $x$ $(x<<1m)$. The particle executes SHM. Its angular frequency of oscillation will be _______ $\times {10}^{5}\mathrm{rad}{s}^{-1}$ (if ${q}^{2}=10{C}^{2}$)

A circular coil of radius $8.0\mathrm{cm}$ and $20$ turns is rotated about its vertical diameter with an angular speed of $50\mathrm{rad}{s}^{-1}$ in a uniform horizontal magnetic field of $3.0\times {10}^{-2}T$. The maximum emf induced in the coil will be _______$\times {10}^{-2}$ volt (rounded off to the nearest integer).

At very high frequencies, the effective impedance of the given circuit will be _________$\Omega .$ 

A series LCR circuit of $R=5\Omega ,L=20\mathrm{mH}$ and $C=0.5\mu F$ is connected across an $\mathrm{AC}$ supply of $250V,$ having variable frequency. The power dissipated at resonance condition is ________$\times {10}^{2}W.$

What happens to the inductive reactance and the current in a purely inductive circuit if the frequency is halved ?

The wavelength of an X-ray beam is $10Å$. The mass of a fictitious particle having the same energy as that of the X-ray photons is $\frac{x}{3}h\mathrm{kg}.$ The value of $x$ is ___ . ($h=$Planck's constant)

A current of $1.5A$ is flowing through a triangle, of side $9\mathrm{cm}$ each. The magnetic field at the centroid of the triangle is : (Assume that the current is flowing in the clockwise direction.)

The electric field in a region is given by $\vec{E}=(\frac{3}{5}{E}_{0}\hat{i}+\frac{4}{5}{E}_{0}\hat{j})N{C}^{-1}$. The ratio of flux of reported field through the rectangular surface of area $0.2{m}^{2}$ (parallel to $y-z$ plane) to that of the surface of area $0.3{m}^{2}$ (parallel to $x-z$ plane) is $a:b=a:2,$ where $a=?$ [Here $\hat{i},\hat{j}$ and $\hat{k}$ are unit vectors along $x,y$ and $z$ -axes respectively]

Match List I with List II. <table class="pyq-table"><tbody><tr><td></td><td>List I</td><td></td><td>List II</td></tr><tr><td>(a)</td><td>Rectifier</td><td>(i)</td><td>Used either for stepping up or stepping down the A.C. voltage</td></tr><tr><td>(b)</td><td>Stabilizer</td><td>(ii)</td><td>Used to convert A.C. voltage into D.C. voltage</td></tr><tr><td>(c)</td><td>Transformer</td><td>(iii)</td><td>Used to remove any ripple in the rectified output voltage</td></tr><tr><td>(d)</td><td>Filter</td><td>(iv)</td><td>Used for constant output voltage even when the input voltage or load current change</td></tr></tbody></table>Choose the correct answer from the options given below:

A point charge of $+12\mu C$ is at a distance $6\mathrm{cm}$ vertically above the centre of a square of side $12\mathrm{cm}$ as shown in figure. The magnitude of the electric flux through the square will be _______ $\times {10}^{3}N{m}^{2}{C}^{-1}.$ 

Two capacitors of capacities $2C$ and $C$ are joined in parallel and charged up to potential $V.$ The battery is removed and the capacitor of capacity $C$ is filled completely with a medium of dielectric constant $K.$ The potential difference across the capacitors will now be:

In the given circuit the $\mathrm{AC}$ source has $\omega =100\mathrm{rad}{s}^{-1}$. Considering the inductor and capacitor to be ideal, what will be the current $I$ flowing through the circuit? 

Four identical long solenoids $A,B,C$ and $D$ are connected to each other as shown in the figure. If the magnetic field at the center of $A$ is $3T$ the field at the center of $C$ would be : (Assume that the magnetic field is confined with in the volume of respective solenoid). 

$AC$ voltage $V(t)=20\mathrm{sin}\omega t$ of frequency $50\mathrm{Hz}$ is applied to a parallel plate capacitor. The separation between the plates is $2\mathrm{mm}$ and the area is $1{m}^{2}$. The amplitude of the oscillating displacement current for the applied $AC$ voltage is $[\text{Take }{\epsilon }_{0}=8.85\times {10}^{-12}F{m}^{-1}]$

A $16\Omega$ wire is bent to form a square loop. A $9V$ supply having an internal resistance of $1\Omega$ is connected across one of its sides. The potential drop across the diagonals of the square loop is __________$\times {10}^{-1}V$.

In an ac circuit, an inductor, a capacitor and a resistor are connected in series with ${X}_{L}=R={X}_{C}.$ Impedance of this circuit is :

An alternating current is given by the equation $i={i}_{1}\mathrm{sin}\omega t+{i}_{2}\mathrm{cos}\omega t$. The rms current will be:

A constant magnetic field of $1T$ is applied in the $x>0$ region. A metallic circular ring of radius $1m$ is moving with a constant velocity of $1m{s}^{-1}$ along the $x$-axis. At $t=0s$, the centre $O$ of the ring is at $x=-1m$. What will be the value of the induced emf in the ring at $t=1s$ ? (Assume the velocity of the ring does not change.) 

In a circuit consisting of a capacitance and a generator with alternating emf, ${E}_{g}={E}_{go}sin\omega t,{V}_{C}$ and ${I}_{C}$ are the voltage and current. Correct phasor diagram for such circuit is 

Two particles $A$ and $B$ having charges $20\mu C$ and $-5\mu C$ respectively are held fixed with a separation of $5\mathrm{cm}$ At what position a third charged particle should be placed so that it does not experience a net electric force ? 

A conducting bar of length $L$ is free to slide on two parallel conducting rails as shown in the figure  Two resistors ${R}_{1}$ and ${R}_{2}$ are connected across the ends of the rails. There is a uniform magnetic field $\vec{B}$ pointing into the page. An external agent pulls the bar to the left at a constant speed $v$. The correct statement about the directions of induced currents ${I}_{1}$ and ${I}_{2}$ flowing through ${R}_{1}$ and ${R}_{2}$ respectively is :

An $L.C.R.$ circuit contains resistance of $110\Omega$ and a supply of $220V$ at $300\mathrm{rad}{s}^{-1}$ angular frequency. If only capacitance is removed from the circuit, current lags behind the voltage by $45^{\circ}$. If on the other hand, the only the inductor is removed the current leads by $45^{\circ}$ with the applied voltage. The $R.M.S.$ current flowing in the circuit will be:

An electromagnetic wave of frequency $5\mathrm{GHz}$, is travelling in a medium whose relative electric permittivity and relative magnetic permeability both are $2.$ Its velocity in this medium is _______$\times {10}^{7}m{s}^{-1}$.

Find the peak current and resonant frequency of the following circuit (as shown in figure). 

The current $(i)$ at time $t=0$ and $t=\infty$ respectively for the given circuit is : 

A cube of side $a$ has point charges $+Q$ located at each of its vertices except at the origin where the charge is $-Q.$ The electric field at the centre of cube is: 

An inductor coil stores $64J$ of magnetic field energy and dissipates energy at the rate of $640W$ when a current of $8A$ is passed through it. If this coil is joined across an ideal battery, find the time constant of the circuit (in $s$).

The relative permittivity of distilled water is $81.$ The velocity of light in it will be: $($Given ${\mu }_{r}=1)$

Magnetic fields at two points on the axis of a circular coil at a distance of $0.05m$ and $0.2m$ from the centre are in the ratio $8:1$. The radius of coil is _______ .

A plane electromagnetic wave with a frequency of $30\mathrm{MHz}$ travels in free space. At a particular point in space and time, the electric field is $6V{m}^{-1}$. The magnetic field at this point will be $x\times {10}^{-8}T$. The value of $x$ is,

A plane electromagnetic wave of frequency $500\mathrm{MHz}$ is traveling in a vacuum along the $y-$direction. At a particular point in space and time, $\vec{B}=8.0\times {10}^{-8}\hat{z}T$. The value of the electric field at this point is:(speed of light $=3\times {10}^{8}{\mathrm{ms}}^{-1}$) $\hat{x},\hat{y},\hat{z}$ are unit vectors along $x,y$ and $z$ direction.

A square loop of side $20\mathrm{cm}$ and resistance $1\Omega$ is moved towards right with a constant speed ${v}_{0}.$ The right arm of the loop is in a uniform magnetic field of $5T.$ The field is perpendicular to the plane of the loop and is going into it. The loop is connected to a network of resistors each of value $4\Omega .$ What should be the value of ${v}_{0}$ so that a steady current of $2\mathrm{mA}$ flows in the loop ? 

Match List-I with List-II. <table class="pyq-table"><tbody><tr><td></td><td>List - I</td><td></td><td>List - II</td></tr><tr><td>(a)</td><td>$\omega L>\frac{1}{\omega C}$</td><td>(i)</td><td>Current is in phase with emf</td></tr><tr><td>(b)</td><td>$\omega L=\frac{1}{\omega C}$</td><td>(ii)</td><td>Current lags behind the applied emf</td></tr><tr><td>(c)</td><td>$\omega L<\frac{1}{\omega C}$</td><td>(iii)</td><td>Maximum current occurs</td></tr><tr><td>(d)</td><td>Resonant frequency</td><td>(iv)</td><td>Current leads the emf</td></tr></tbody></table>Choose the correct answer from the options given below.

A charge $q$ is placed at one corner of a cube as shown in figure. The flux of electrostatic field $\vec{E}$ through the shaded area is: 

$512$ identical drops of mercury are charged to a potential of $2V$ each. The drops are joined to form a single drop. The potential of this drop is $V$ in Volt.

The magnetic field in a region is given by $\vec{B}={B}_{0}(\frac{x}{a})\hat{k}$. A square loop of side d is placed with its edges along the $x$ and $y$ axes. The loop is moved with a constant velocity $\vec{v}={v}_{0}\hat{i}$. The emf induced in the loop is : 

The figure shows a circuit that contains four identical resistors with resistance $R=2.0\Omega ,$ two identical inductors with inductance $L=2.0\mathrm{mH}$ and an ideal battery with E.M.F. $E=9V.$ The current $i$ just after the switch $S$ is closed will be: 

For the given circuit, comment on the type of transformer used : 

A common transistor radio set requires $12V$ $(D.C.)$ for its operation. The $D.C.$ source is constructed by using a transformer and a rectifier circuit, which are operated at $220V$ $(A.C.)$ on standard domestic $A.C.$ supply. The number of turns of secondary coil are $24,$ then the number of turns of primary are

An $AC$ current is given by $I={I}_{1}sin\omega t+{I}_{2}cos\omega t.$ A hot wire ammeter will give a reading:

In a scries $LCR$ resonance circuit, if we change the resistance only, from a lower to higher value :

Two ions having same mass have charges in the ratio $1:2$. They are projected normally in a uniform magnetic field with their speeds in the ratio $2:3$. The ratio of the radii of their circular trajectories is,

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

Two short magnetic dipoles ${m}_{1}$ and ${m}_{2}$ each having magnetic moment of $1A{m}^{2}$ are placed at point $O$ and $P$ respectively. The distance between $OP$ is $1m$. The torque experienced by the magnetic dipole ${m}_{2}$ due to the presence of ${m}_{1}$ is $________\times {10}^{-7}Nm$ 

Intensity of sunlight is observed as $0.092{\mathrm{Wm}}^{-2}$ at a point in free space. What will be the peak value of magnetic field at that point ? $({\epsilon }_{0}=8.85\times {10}^{-12}{C}^{2}{N}^{-1}{m}^{-2})$

An electron with kinetic energy ${K}_{1}$ enters between parallel plates of a capacitor at an angle $\alpha$ with the plates. It leaves the plates at angle $\beta$ with kinetic energy ${K}_{2}.$ Then the ratio of kinetic energies ${K}_{1}:{K}_{2}$ will be :

The peak electric field produced by the radiation coming from the $8W$ bulb at a distance of $10m$ is $\frac{x}{10}\sqrt{\frac{{\mu }_{0}c}{\pi }}V{m}^{-1}$. The efficiency of the bulb is $10%$ and it is a point source. The value of $x$ is,

In an electromagnetic wave, the electric field vector and magnetic field vector are given as $\vec{E}={E}_{0}\hat{i}$ and $\vec{B}={B}_{0}\hat{k}$, respectively. The direction of propagation of electromagnetic wave is along:

Calculate the amount of charge on capacitor of $4\mu F.$ The internal resistance of battery is $1\Omega :$ 

$27$ similar drops of mercury are maintained at $10V$ each. All these spherical drops combine into a single big drop. The potential energy of the bigger drop is ___________ times that of a smaller drop.

A coil in the shape of an equilateral triangle of side $10\mathrm{cm}$ lies in a vertical plane between the pole pieces of permanent magnet producing a horizontal magnetic field $20\mathrm{mT}$. The torque acting on the coil when a current of $0.2A$ is passed through it and its plane becomes parallel to the magnetic field will be $\sqrt{x}\times {10}^{-5}\mathrm{Nm}$. The value of $x$ is

There are two infinitely long straight current-carrying conductors and they are held at right angles to each other so that their common ends meet at the origin as shown in the figure given below. The ratio of current in both conductors is $1:1$. The magnetic field at point $P$ is$_________.$ 

For changing the capacitance of a given paralle plate capacitor, a dielectric material of dielectric constant $K$ is used, which has the same area as the plates of the capacitor. The thickness of the dielectric slab is $\frac{3}{4}d$, where $d$ is the separation between the plates of parallel plate capacitor. The new capacitance ${C}^{'}$ in terms of original capacitance ${C}_{0}$ is given by the following relation :

A certain charge $Q$ is divided into two parts $q$ and $(Q-q).$ How should the charges $Q$ and $q$ be divided so that $q$ and $(Q-q)$ placed at a certain distance apart experience maximum electrostatic repulsion?

The alternating current is given by, $i={\sqrt{42}\mathrm{sin}(\frac{2\pi }{T}t)+10}A$. The R.M.S. value of this current is __________ $A$.

The resistance of a conductor at $15^{\circ}C$ is $16\Omega$ and at $100^{\circ}C$ is $20\Omega .$ What will be the temperature coefficient of resistance of the conductor?

For full scale deflection of total $50$ divisions, $50\mathrm{mV}$ voltage is required in galvanometer. The resistance of galvanometer if its current sensitivity is $2\mathrm{div}/\mathrm{mA}$ will be:

In a parallel plate capacitor set up, the plate area of capacitor is $2{m}^{2}$ and the plates are separated by $1m$. If the space between the plates are filled with a dielectric material of thickness $0.5m$ and are $2{m}^{2}$ (see figure) the capacitance of the set-up will be ${\epsilon }_{0}$ ________. (Dielectric constant of the material $=3.2$) (Round off to the Nearest Integer) 

A current of $6A$ enters one corner $P$ of an equilateral triangle $PQR$ having $3$ wires of resistance $2\Omega$ each and leaves by the corner $R.$ The currents ${i}_{1}$ in ampere is 

Two electrons each are fixed at a distance $2d.$ A third charge proton placed at the midpoint is displaced slightly by a distance $x(x\ll d)$ perpendicular to the line joining the two fixed charges. Proton will execute simple harmonic motion having angular frequency: ($m=$ mass of charged particle)

In a ferromagnetic material, below the curie temperature, a domain is defined as:

A resistor dissipates $192J$ of energy in $1s$ when a current of $4A$ is passed through it. Now, when the current is doubled, the amount of thermal energy dissipated in $5s$ is _____________ $J.$

An X-ray tube is operated at $1.24$ million volt. The shortest wavelength of the produced photon will be:

An electric bulb of $500W$ at $100V$ is used in a circuit having a $200V$ supply. Calculate the resistance $R$ to be connected in series with the bulb so that the power delivered by the bulb is $500W$.

The voltage across the $10\Omega$ resistor in the given circuit is $x$ volt.  The value of $x$ to the nearest integer is _____.

Consider a galvanometer shunted with $5\Omega$ resistance and $2%$ of current passes through it. What is the resistance of the given galvanometer?

Find out the surface charge density at the intersection of point $x=3m$ plane and $x$-axis, in the region of uniform line charge of $8\mathrm{nC}{m}^{-1}$ lying along the $z$-axis in free space.

Consider a $72\mathrm{cm}$ long wire $AB$ as shown in the figure. The galvanometer jockey is placed at $P$ on $AB$ at a distance $x\mathrm{cm}$ from $A$. The galvanometer shows zero deflection.  The value of $x$, to the nearest integer, is

A parallel plate capacitor with plate area '$A$' and distance of separation '$d$' is filled with a dielectric. What is the capacity of the capacitor when permittivity of the dielectric varies as: $\epsilon (x)={\epsilon }_{0}+kx$, for $(0<x\leq \frac{d}{2})$ $\epsilon (x)={\epsilon }_{0}+k(d-x)$, for $(\frac{d}{2}\leq x\leq d)$

A resistor develops $500J$ of thermal energy in $20s$ when a current of $1.5A$ is passed through it. If the current is increased from $1.5A$ to $3A$, what will be the energy developed in $20s$.

The angular frequency of alternating current in a L-C-R circuit is $100\mathrm{rad}{s}^{-1}$. The components connected are shown in the figure. Find the value of inductance of the coil and capacity of condenser. 

A uniform conducting wire of length is $24a,$ and resistance $R$ is wound up as a current carrying coil in the shape of an equilateral triangle of side $a$ and then in the form of a square of side $a$. The coil is connected to a voltage source ${V}_{0}.$ The ratio of magnetic moment of the coils in case of equilateral triangle to that for square is $1:\sqrt{y}$ where $y$ is ____________.

The equivalent resistance of the given circuit between the terminals $A$ and $B$ is : 

A coaxial cable consists of an inner wire of radius $a$ surrounded by an outer shell of inner and outer radii $b$ and $c$ respectively. The inner wire carries an electric current ${i}_{0}$ which is distributed uniformly across cross-sectional area. The outer shell carries an equal current in opposite direction and distributed uniformly. What will be the ratio of the magnetic field at a distance $x$ from the axis when $(i)$ $x<a$ and $(ii)$ $a<x<b$ ?

The equivalent resistance of series combination of two resistors is $s.$ When they are connected in parallel, the equivalent resistance is $p.$ If $s=np,$ then the minimum value for $n$ is ______. (Round off to the Nearest Integer)

A cell ${E}_{1}$ of emf $6V$ and internal resistance $2\Omega$ is connected with another cell ${E}_{2}$ of emf $4V$ and internal resistance $8\Omega$ (as shown in the figure). The potential difference across points $X$ and $Y$ is: 

Choose the incorrect statement: (a) The electric lines of force entering into a Gaussian surface provide negative flux. (b) A charge $q$ is placed at the centre of a cube. The flux through all the faces will be the same. (c) In a uniform electric field net flux through a closed Gaussian surface containing no net charge, is zero. (d) When an electric field is parallel to a Gaussian surface, it provides a finite non-zero flux. Choose the most appropriate answer from the options given below:

An electric bulb rated as $200W$ at $100V$ is used in a circuit having $200V$ supply. The resistance $R$ that must be put in series with the bulb so that the bulb delivers the same power is ______ $\Omega$.

A $0.07H$ inductor and a $12\Omega$ resistor are connected in series to a $220V,50\mathrm{Hz}$ AC source. The approximate current in the circuit and the phase angle between current and source voltage are respectively. [Take $\pi$ as $\frac{22}{7}]$

An electromagnetic wave of frequency $3\mathrm{GHz}$ enters a dielectric medium of relative electric permittivity $2.25$ from vacuum. The wavelength of this wave in that medium will be _________ $\times {10}^{-2}\mathrm{cm}.$

A transmitting station releases waves of wavelength $960m$. A capacitor of $2.56\mu F$ is used in the resonant circuit. The self-inductance of coil necessary for resonance is $x\times {10}^{-8}H$. find $x$

Two equal capacitors are first connected in series and then in parallel. The ratio of the equivalent capacities in the two cases will be:

A cylindrical wire of radius $0.5\mathrm{mm}$ and conductivity $5\times {10}^{7}S{m}^{-1}$ is subjected to an electric field of $10\mathrm{mV}{m}^{-1}.$ The expected value of current in the wire will be ${x}^{3}\pi \mathrm{mA}.$ The value of $x$ is _________.

A cube is placed inside an electric field, $\vec{E}=150{y}^{2}\hat{j}$ The side of the cube is $0.5m$ and is placed in the field as shown in the given figure. The charge inside the cube is: 

A uniformly charged disc of radius $R$ having surface charge density $\sigma$ is placed in the $xy$ plane with its center at the origin. Find the electric field intensity along the $z$-axis at a distance $Z$ from origin:

Figure shows a rod $AB$, which is bent in a $120^{\circ}$ circular arc of radius $R$. A charge$(-Q)$ is uniformly distributed over rod $\mathrm{AB}$. What is the electric filed $\vec{E}$ at the centre of curvature $O$ ? 

The two thin coaxial rings, each of radius $a$ and having charges $+Q$ and $-Q$ respectively are separated by a distance of $s$. The potential difference between the centres of the two rings is :

What will be the magnitude of the electric field at point $O$ as shown in the figure? Each side of the figure is $l$ and perpendicular to the other? 

A solid metal sphere of radius $R$ having charge $q$ is enclosed inside the concentric spherical shell of inner radius $a$ and outer radius $b$ as shown in the figure. The approximate variation electric field $\vec{E}$, as a function of distance $r$, from centre $O$, is given by: 

A simple pendulum of mass ' $m$ ', length ' $l$ ' and charge $'+{q}^{'}$ suspended in the electric field produced by two conducting parallel plates as shown. The value of deflection of pendulum in equilibrium position will be 

Two small spheres each of mass $10\mathrm{mg}$ are suspended from a point by threads $0.5m$ long. They are equally charged and repel each other to a distance of $0.20m$. The charge on each of the sphere is $\frac{a}{21}\times {10}^{-8}C.$ The value of $a$ will be ___.[Given $g=10m{s}^{-2}$]

Two ideal electric dipoles $A$ and $B$, having their dipole moment ${p}_{1}$ and ${p}_{2}$ respectively are placed on a plane with their centres at $O$ as shown in the figure. At point $C$ on the axis of dipole $A$, the resultant electric field is making an angle of $37^{\circ}$ with the axis. The ratio of the dipole moment of $A$ and $B,\frac{{p}_{1}}{{p}_{2}}$ is$:($ take $\mathrm{sin}37^{\circ}=\frac{3}{5})$ 

The total charge enclosed in an incremental volume of $2\times {10}^{-9}{m}^{3}$ located at the origin is $\mathrm{nC},$ if electric flux density of its field is found as$D={e}^{-x}\mathrm{sin}y\hat{i}-{e}^{-x}\mathrm{cosy}\hat{j}+2z\hat{k}C{m}^{-2}$

An electric dipole is placed on $x-$axis in proximity to a line charge of linear charge density $3.0\times {10}^{-6}C{m}^{-1}.$ Line charge is placed on $z-$axis and positive and negative charge of dipole is at a distance of $10\mathrm{mm}$ and $12\mathrm{mm}$ from the origin respectively. If total force of $4N$ is exerted on the dipole, find out the amount of positive or negative charge of the dipole.

An infinite number of point charges, each carrying $1\mu C$ charge, are placed along the y-axis at $y=1m,2m,4m,8m....$ The total force on a $1C$ point charge, placed at the origin, is $x\times {10}^{3}N$. The value of $x$, to the nearest integer, is ___ . [Take $\frac{1}{4\pi {\epsilon }_{0}}=9\times {10}^{9}N{m}^{2}{C}^{-2}$]

The electric field intensity is produced by the radiation coming from a $100W$ bulb at a distance of $3m$ is $E$. The electric field intensity produced by the radiation coming from $60W$ at the same distance is $\sqrt{\frac{x}{5}}E$. Where the value of $x=$_________ .

The electric field in a region is given by $\vec{E}=\frac{2}{5}{E}_{0}\hat{i}+\frac{3}{5}{E}_{0}\hat{j}$ with ${E}_{0}=4.0\times {10}^{3}N{C}^{-1}.$ The flux of this field through a rectangular surface, area $0.4{m}^{2}$ parallel to the $Y-Z$ plane is _______ $N{m}^{2}{C}^{-1}$.

Find the electric field at point $P$ (as shown in figure) on the perpendicular bisector of a uniformly charged thin wire of length $L$ carrying a charge $Q$. The distance of the point $P$ from the centre of the rod is $a=\frac{\sqrt{3}}{2}L$ 

Two identical conducting spheres with negligible volume have $2.1\mathrm{nC}$ and $-0.1\mathrm{nC}$ charges, respectively. They are brought into contact and then separated by a distance of $0.5m$. The electrostatic force acting between the spheres is ___$\times {10}^{-9}N$. [Given : $4\pi {\epsilon }_{0}=\frac{1}{9\times {10}^{9}}$ SI unit]

Given below are two statements Statement $I$ : An electric dipole is placed at the centre of a hollow sphere. The flux of electric field through the sphere is zero, but the electric field is not zero anywhere in the sphere. Statement $\mathrm{II}$ : If $R$ is the radius of a solid metallic sphere and $Q$ be the total charge on it. The electric field at any point on the spherical surface of radius $r(<R)$ is zero but the electric flux passing through this closed spherical surface of radius $r$ is not In the light of the above statements, choose the correct answer from the options given below:

In an electrical circuit, a battery is connected to pass $20C$ of charge through it in a certain given time. The potential difference between two plates of the battery is maintained at $15V$. The workdone by the battery is _______ $J$

A $2\mu F$ capacitor ${C}_{1}$ is first charged to a potential difference of $10V$ using a battery. Then the battery is removed and the capacitor is connected to an uncharged capacitor ${C}_{2}$ of $8\mu F$. The charge in ${C}_{2}$ on equilibrium condition is $\mu C$. (Round off to the Nearest Integer) 

A capacitor is connected to a $20V$ battery through a resistance of $10\Omega .$ It is found that the potential difference across the capacitor rises to $2V$ in $1\mu s.$ The capacitance of the capacitor is $________\mu F.$ Given In $(\frac{10}{9})=0.105$

Three capacitors ${C}_{1}=2\mu F,{C}_{2}=6\mu F$ and ${C}_{3}=12\mu F$ are connected as shown in the figure. Find the ratio of the charges on capacitors ${C}_{1},{C}_{2}$ and ${C}_{3}$ respectively. 

A capacitor of $50\mu F$ is connected in a circuit as shown in figure. The charge on the upper plate of the capacitor is _________ $\mu C.$ 

A parallel plate capacitor of capacitance $200\mu F$ is connected to a battery of $200V.$ A dielectric slab of dielectric constant $2$ is now inserted into the space between plates of capacitor while the battery remain connected. The change in the electrostatic energy in the capacitor will be __________ $J.$

In the reported figure, a capacitor is formed by placing a compound dielectric between the plates of parallel plate capacitor. The expression for the capacity of the said capacitor will be: (Given the area of the plate $=A$ ) 

A parallel-plate capacitor with plate area $A$ has separation $d$ between the plates. Two dielectric slabs of dielectric constant ${K}_{1}$ and ${K}_{2}$ of same area $\frac{A}{2}$ and thickness $\frac{d}{2}$ are inserted in the space between the plates. The capacitance of the capacitor will be given by : 

The material filled between the plates of a parallel plate capacitor has resistivity $200\Omega m$. The value of capacitance of the capacitor is $2\mathrm{pF}$. If a potential difference of $40V$ is applied across the plates of the capacitor, then the value of leakage current flowing out of the capacitor is: (given the value of relative permittivity of material is $50$)

A parallel plate capacitor has plate area $100{m}^{2}$ and plate separation of $10m.$ The space between the plates is filled up to a thickness $5m$ with a material of dielectric constant of $10.$ The resultant capacitance of the system is $x\mathrm{pF}.$ The value of ${\epsilon }_{0}=8.85\times {10}^{-12}F{m}^{-1}$. The value of $x$ to the nearest integer is ______.

If ${q}_{f}$ is the free charge on the capacitor plates and ${q}_{b}$ is the bound charge on the dielectric slab of dielectric constant $k$ placed between the capacitor plates, then bound charge ${q}_{b}$ can be expressed as :

 A capacitor of capacitance $C=1\mu F$ is suddenly connected to a battery of $100V$ through a resistance $R=100\Omega .$ The time taken for the capacitor to be charged to get $50V$ is: (Take $\mathrm{ln}2=0.69$)

A parallel plate capacitor whose capacitance $C$ is $14\mathrm{pF}$ is charged by a battery to a potential difference $V=12V$ between its plates. The charging battery is now disconnected and a porcelain plate with $k=7$ is inserted between the plates, then the plate would oscillate back and forth between the plates with a constant mechanical energy of _______ $\mathrm{pJ}.$ (Assume no friction)

Four identical rectangular plates with length, $l=2\mathrm{cm}$ and breadth, $b=\frac{3}{2}\mathrm{cm}$ are arranged as shown in figure. The equivalent capacitance between $A$ and $C$ is $\frac{x{\epsilon }_{0}}{d}.$ The value of $x$ is _______. (Round off to the Nearest Integer) 

Consider the combination of two capacitors ${C}_{1}$ and ${C}_{2}$, with ${C}_{2}>{C}_{1}$, when connected in parallel, the equivalent capacitance is $10$ times the equivalent capacitance of the same connected in series. Calculate the ratio of capacitors, $\frac{{C}_{2}}{{C}_{1}}$.

In the given figure, a battery of emf $E$ is connected across a conductor $PQ$ of length $l$ and different area of cross-sections having radii ${r}_{1}$ and ${r}_{2}({r}_{2}<{r}_{1}).$  Choose the correct option as one moves from $P$ to $Q$.

Two resistors ${R}_{1}=(4\pm 0.8)\Omega$ and ${R}_{2}=(4\pm 0.4)\Omega$ are connected in parallel. The equivalent resistance of their parallel combination will be :

A steel rod with $y=2.0\times {10}^{11}N{m}^{-2}$ and $\alpha ={10}^{-5}{C\circ }^{-1}$ of length $4m$ and area of cross-section $10{\mathrm{cm}}^{2}$ is heated from $0^{\circ}C$ to $400^{\circ}C$ without being allowed to extend. The tension produced in the rod is $x\times {10}^{5}N$ where the value of $x$ is $_________.$

The voltage drop across $15\Omega$ resistance in the given figure will be _______ $V.$ 

A square-shaped wire with a resistance of each side $3\Omega$ is bent to form a complete circle. The resistance between two diametrically opposite points of the circle in a unit of $\Omega$ will is, _____.

In the given figure switches ${S}_{1}$ and ${S}_{2}$ are in open condition. The resistance across $ab$ when the switches ${S}_{1}$ and ${S}_{2}$ are closed is ________$\Omega .$ 

The ratio of the equivalent resistance of the network (shown in figure) between the points $a$ and $b$ when switch is open and switch is closed is $x:8$. The value of $x$ is 

First, a set of $n$ equal resistors of $10\Omega$ each are connected in series to a battery of E.M.F. $20V$ and internal resistance $10\Omega .$ A current $I$ is observed to flow. Then, the $n$ resistors are connected in parallel to the same battery. It is observed that the current is increased $20$ times, then the value of $n$ is ___________.

If you are provided a set of resistances, $2\Omega ,4\Omega ,6\Omega$ and $8\Omega .$ Connect these resistances to obtain an equivalent resistance of $\frac{46}{3}\Omega$.

Five identical cells each of internal resistance $1\Omega$ and emf $5V$ are connected in series and in parallel with an external resistance $R.$ For what value of $R,$ current in series and parallel combination will remain the same?

For the circuit shown, the value of current at time $t=3.2s$ will be ______ $A$.  [Voltage distribution $V(t)$ is shown by Fig. $(1)$ and the circuit is shown in Fig. $(2)$]

What equal length of an iron wire and a copper-nickel alloy wire, each of $2\mathrm{mm}$ diameter connected parallel to give an equivalent resistance of $3\Omega$? (Given resistivities of iron and copper-nickel alloy wire are $12\mu \Omega \mathrm{cm}$ and $51\mu \Omega \mathrm{cm}$ respectively)

In the given figure, the emf of the cell is $2.2V$ and if internal resistance is $0.6\Omega$. Calculate the power dissipated in the whole circuit: 

A Copper $(\mathrm{Cu})$ rod of length $25\mathrm{cm}$ and cross-sectional area $3{\mathrm{mm}}^{2}$ is joined with a similar Aluminium $(\mathrm{Al})$ rod as shown in figure. Find the resistance of the combination between the ends $A$ and $B.$ (Take resistivity of Copper $=1.7\times {10}^{-8}\Omega m$, Resistivity of aluminium $=2.6\times {10}^{-8}\Omega m$) 

In an electric circuit, a call of certain emf provides a potential difference of $1.25V$ across a load resistance of $5\Omega .$ However, it provides a potential difference of $1V$ across a load resistance of $2\Omega .$The emf of the cell is given by $\frac{x}{10}V.$ Then the value of $x$ is $.$

A current of $5A$ is passing through a non-linear magnesium wire of cross-section $0.04{m}^{2}$. At every point the direction of current density is at an angle of $60^{\circ}$ with the unit vector of area of cross-section. The magnitude of electric field at every point of the conductor is: (resistivity of magnesium $\rho =44\times {10}^{-8}\Omega m$)

 The value of current in the $6\Omega$ resistance is:

Seawater at a frequency $f=9\times {10}^{2}\mathrm{Hz}$, has permittivity $\epsilon =80{\epsilon }_{0}$ and resistivity $\rho =0.25\Omega m$. Imagine a parallel plate capacitor is immersed in seawater and is driven by an alternating voltage source $V(t)={V}_{0}\mathrm{sin}(2\pi ft)$. Then the conduction current density becomes ${10}^{x}$ times the displacement current density after time $t=\frac{1}{800}s.$ The value of $x$ is _______ (Given $:\frac{1}{4\pi {\epsilon }_{0}}=9\times {10}^{9}N{m}^{2}{C}^{-2})$

The four arms of a Wheatstone bridge have resistances as shown in the figure. A galvanometer of $15\Omega$ resistance is connected across BD. Calculate the current through the galvanometer when a potential difference of $10V$ is maintained across AC. 

The circuit shown in the figure consists of a charged capacitor of capacity $3\mu F$ and a charge of $30\mu C.$ At time $t=0,$ when the key is closed, the value of current flowing through the $5M\Omega$ resistor is $x\mu A.$ The value of $x$ to the nearest integer is 

In the experiment of Ohm's law, a potential difference of $5.0V$ is applied across the end of a conductor of length $10.0\mathrm{cm}$ and diameter of $5.00\mathrm{mm}.$ The measured current in the conductor is $2.00A.$ The maximum permissible percentage error in the resistivity of the conductor is :-

The energy dissipated by a resistor is $10\mathrm{mJ}$ in $1s$, when an electric current of $2\mathrm{mA}$ flows through it. The resistance is ________$\Omega$. (Round off to the Nearest Integer)

A current of $10A$ exists in a wire of cross-sectional area of $5{\mathrm{mm}}^{2}$ with a drift velocity of $2\times {10}^{-3}{ms}^{-1}.$ The number of free electrons in each cubic meter of the wire is

Two cells of emf $2E$ and $E$ with internal resistance ${r}_{1}$and ${r}_{2}$ respectively are connected in series to an external resistor $R$ (see figure). The value of $R,$ at which the potential difference across the terminals of the first cell becomes zero is 

In the figure given, the electric current flowing through the $5k\Omega$ resistor is $x$ $\mathrm{mA}$.  The value of $x$ to the nearest integer is ________.

Five equal resistances are connected in a network as shown in figure. The net resistance between the points $A$ and $B$ is : 

A conducting wire of length $l$, area of crosssection $A$ and electric resistivity $\rho$ is connected between the terminals of a battery. A potential difference $V$ is developed between its ends, causing an electric current. If the length of the wire of the same material is doubled and the area of cross-section is halved, the resultant current would be___

A current through a wire depends on time as $i={\alpha }_{0}t+\beta {t}^{2}$, where ${\alpha }_{0}=20A{s}^{-1}$ and $\beta =8A{s}^{-2}$. Find the charge crossed through a section of the wire in $15s.$

Following plots show Magnetization $(M)$ vs Magnetising field $(H)$ and Magnetic susceptibility $(\chi )$ vs Temperature $(T)$ graph :  Which of the following combination will be represented by a diamagnetic material?

In a uniform magnetic field, the magnetic needle has a magnetic moment $9.85\times {10}^{-2}A{m}^{-2}$ and moment of inertia $5\times {10}^{-6}\mathrm{kg}{m}^{2}.$ If it performs $10$ complete oscillations in $5$ seconds then the magnitude of the magnetic field is ____$\mathrm{mT}$ [Take ${\pi }^{2}$ as $9.85]$

Statement I : The ferromagnetic property depends on temperature. At high temperature, ferromagnet becomes paramagnet. Statement II : At high temperature, the domain wall area of a ferromagnetic substance increases. In the light of the above statements, choose the most appropriate answer from the options given below:

Which of the following statements are correct? (A) Electric monopoles do not exist whereas magnetic monopoles exist. (B) Magnetic field lines due to a solenoid at its ends and outside cannot be completely straight and confined. (C) Magnetic field lines are completely confined within a toroid. (D) Magnetic field lines inside a bar magnet are not parallel. (E) $\chi =-1$ is the condition for a perfect diamagnetic material, where $\chi$ is its magnetic susceptibility. Choose the correct answer from the options given below :

A soft ferromagnetic material is placed in an external magnetic field. The magnetic domains: