Electromagnetism PYQ — Page 53

A capacitor with capacitance $5 \mu F$ is charged to $5 \mu C$ . If the plates are pulled apart to reduce the capacitance to $2 \mu F$, how much work is done?

Two magnetic dipoles $X$ and $Y$ are placed at a separation $d$ , with their axes perpendicular to each other. The dipole moment of $Y$ is twice that of $X$ . A particle of charge $q$ is passing through their mid-point $P$ , at angle $\theta ={45}^{o}$ with the horizontal line, as shown in figure. What would be the magnitude of force on the particle at that instant? ( $d$ is much larger than the dimension of the dipole) 

In the given circuit diagram, the currents, ${I}_{1}=-0.3 A, {I}_{4}=0.8 A$ and ${I}_{5}=0.4 A,$ are flowing as shown. The currents ${I}_{2}, {I}_{3}$ and ${I}_{6},$ respectively, are: 

Space between two concentric conducting spheres of radii $a$ and $b$ $(b>a)$ is filled with a medium of resistivity $\rho$ . The resistance between the two spheres will be:

In the given circuit, an ideal voltmeter connected across the $10 \Omega$ resistance reads $2 V$ . The internal resistance $r$ , of each cell is: 

A metal wire of resistance $3 \Omega$ is elongated to make a uniform wire of double its previous length. This new wire is now bent and the ends joined to make a circle. If two points on this circle make an angle ${60}^{o}$ at the center, the equivalent resistance between these two points will be:

Two electric bulbs, rated at $(25 W, 220V)$ and $(100 W, 220V),$ are connected in series across a $220\text{V}$ voltage source. If the $25 W$ and $100 W$ bulbs draw powers ${P}_{1}$ and ${P}_{2}$ respectively, then:

In the circuit shown, the potential difference between $\mathrm{A}$ and $B$ is 

A paramagnetic material has ${10}^{28}\mathrm{atoms}{m}^{-3}$. Its magnetic susceptibility at temperature $350 K$ is $2.8×{10}^{-4}$. Its susceptibility at $300 K$ is

A series $AC$ circuit containing an inductor $(20 \mathrm{mH}),$ a capacitor $(120\text{ μ}F)$ and a resistor $(60 \Omega )$ is driven by an $AC$ source of $24 V/50 \mathrm{Hz}.$ The energy dissipated in the circuit in $60 s$ is:

A system of three charges are placed as shown in the figure:  If $D >> d,$ the potential energy of the system is best given by:

A parallel plate capacitor has $1\mu F$ capacitance. One of its two plates is given $+2\mu C$ charge and the other plate, $+4 \mu C$ charge. The potential difference developed across the capacitor is:

The galvanometer deflection, when key ${K}_{1}$ is closed but ${K}_{2}$ is open, equals ${\theta }_{0}$ (see figure). On closing ${K}_{2}$ also and adjusting ${R}_{2}$ to $5\Omega ,$ the deflection in galvanometer becomes $\frac{{\theta }_{0}}{5}.$ The resistance of the galvanometer is, then, given by [Neglect the internal resistance of battery]: 

Two point charges ${q}_{1}(\sqrt{10} \mu C)$ and ${q}_{2}(-25 \mu C)$ are placed on the $x$ -axis at $x=1 m$ and $x=4 m$ respectively. The electric field $(\text{in} V/m)$ at a point $y=3 m$ on $y$-axis is, $[\text{Take}\frac{1}{4\pi {\epsilon }_{0}}=9\times {10}^{9} N{m}^{2}{C}^{-2}]$

In the given circuit the internal resistance of the $18V$ cell is negligible. If ${R}_{1}=400 \Omega , {R}_{3}=100 \Omega$ and ${R}_{4}=500 \Omega$ and the reading of an ideal voltmeter across ${R}_{4}$ is $5 V,$ then the value of ${R}_{2}$ will be: 

Two identical parallel plate capacitors, of capacitance $C$ each, have plates of area $A,$ separated by a distance $d$ . The space between the plates of the two capacitors, is filled with three dielectrics, of equal thickness and dielectric constants ${K}_{1}, {K}_{2}$ and ${K}_{3}$ . The first capaciitor is filled as shown in figure $I,$ and the second one is filled as shown in figure $II.$ If these two modified capacitors are charged by the same potential $V$ , the ratio of the energy stored in the two, would be $({E}_{1}$ refers to capacitor $(I)$ and ${E}_{2}$ to capacitor $(II)$ ): 

A current of $2 \mathrm{mA}$ was passed through an unknown resistor which dissipated a power of $4.4 W.$ Dissipated power when an ideal power supply of $11 V$ is connected across it is:

Two coils $'P'$ and $'Q'$ are separated by some distance. When a current of $3 A$ flows through coil $'{P}^{'},$ a magnetic flux of ${10}^{-3} Wb$ passes through $'{Q}^{'}.$ No current is passed through $'{Q}^{'}.$ When no current passes through $'P'$ and a current of $2 A$ passes through $'{Q}^{'},$ the flux through $'P'$ is:

Two equal resistances when connected in series to a battery, consume electric power of $60 \mathrm{~W}$. If these resistance are now connected in parallel combination to the same battery, the electric power consumed will be :

A very long solenoid of radius $R$ is carrying current $I(t)=kt{e}^{-\alpha t}(k>0),$ as a function of time $(t\geq 0).$ Counterclockwise current is taken to be positive. A circular conducting coil of radius $2R$ is placed in the equitorial plane of the solenoid and concentric with the solenoid. The current induced in the outer coil is correctly depicted, as a function of time, by:

Charge is distributed within a sphere of radius $R$ with a volume charge density $\rho (r)=\frac{A}{{r}^{2}}{e}^{-\frac{2r}{a}},$ where $A$ and $a$ are constants. If $Q$ is the total charge of this charge distribution, the radius $R$ is:

The given graph shows variation (with distancer from centre) of: 

A parallel plate capacitor with square plates is filled with four dielectrics of dielectric constants ${K}_{1}, {K}_{2}, {K}_{3}, {K}_{4}$ arranged as shown in the figure. The effective dielectric constant $K$ will be: 

Mobility of electrons in a semiconductor is defined as the ratio of their drift velocity to the applied electric field. If, for an $\text{N}$-type semiconductor, the density of electrons is ${10}^{19} {m}^{-3}$ and their mobility is $1.6 {m}^{2}{V}^{-1}{s}^{-1}$, then the resistivity of the semiconductor (since it is an $\text{N}$-type semiconductor contribution of holes is ignored) is close to: