Electromagnetism PYQ — Page 36

Two capacitors having capacitance ${C}_{1}$ and ${C}_{2}$ respectively are connected as shown in figure. Initially, capacitor ${C}_{1}$ is charged to a potential difference $V$ volt by a battery. The battery is then removed and the charged capacitor ${C}_{1}$ is now connected to uncharged capacitor ${C}_{2}$ by closing the switch $S$. The amount of charge on the capacitor ${C}_{2}$, after equilibrium, is 

The total current supplied to the circuit as shown in figure by the $5V$ battery is _____ $A$. 

To increase the resonant frequency in series LCR circuit,

A battery of $6V$ is connected to the circuit as shown below. The current $I$ drawn from the battery is 

For a series $LCR$ circuit, $I$ vs $\omega$ curve is shown  (a) To the left of ${\omega }_{r}$, the circuit is mainly capacitive. (b) To the left of ${\omega }_{r}$, the circuit is mainly inductive. (c) At ${\omega }_{r}$, impedance of the circuit is equal to the resistance of the circuit. (d) At ${\omega }_{r}$, impedance of the circuit is $0$. Choose the most appropriate answer from the options given below.

$27$ identical drops are charged at $22V$ each. They combine to form a bigger drop. The potential of the bigger drop will be _____ $V$.

A current of $15\mathrm{mA}$ flows in the circuit as shown in figure. The value of potential difference between the points $A$ and $B$ will be 

A deuteron and a proton moving with equal kinetic energy enter into to a uniform magnetic field at right angle to the field. If ${r}_{d}$ and ${r}_{p}$ are the radii of their circular paths respectively, then the ratio $\frac{{r}_{d}}{{r}_{p}}$ will be $\sqrt{x}:1$ where $x$ is _____ .

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 

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 $2\mu F$ 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 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 ________ $\Omega .$

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: 

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 :

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:

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 ___________.

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 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 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 ? 

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 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 ${\epsilon }_{0}=8.85\times {10}^{-12}{C}^{2}{N}^{-1}{m}^{-2},c=3\times {10}^{6}m{s}^{-1}$]

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). 

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 

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$R=8.31J{\mathrm{mol}}^{-1}{K}^{-1})$