Electromagnetism PYQ — Page 16

To determine the resistance $(R)$ of a wire, a circuit is designed below. The $V-I$ characteristic curve for this circuit is plotted for the voltmeter and the ammeter readings as shown in figure. The value of $R$ is ______ $\Omega$. 

A parallel plate capacitor with plate separation $5\mathrm{mm}$ is charged up by a battery. It is found that on introducing a dielectric sheet of thickness $2\mathrm{mm}$, while keeping the battery connections intact, the capacitor draws $25%$ more charge from the battery than before. The dielectric constant of the sheet is ____.

A rectangular loop of sides $12\mathrm{cm}$ and $5\mathrm{cm}$, with its sides parallel to the $x$-axis and $y$-axis respectively moves with a velocity of $5\mathrm{cm}{s}^{-1}$ in the positive $x$ axis direction, in a space containing a variable magnetic field in the positive $z$ direction. The field has a gradient of ${10}^{-3}T{\mathrm{cm}}^{-1}$ along the negative $x$ direction and it is decreasing with time at the rate of ${10}^{-3}T{s}^{-1}.$ If the resistance of the loop is $6m\Omega$, the power dissipated by the loop as heat is ______ $\times {10}^{-9}W.$

Match List I with List II  $\text { Choose the correct answer from the options given below: }$

The magnetic field at the centre of a wire loop formed by two semicircular wires of radii ${R}_{1}=2\pi m$ and ${R}_{2}=4\pi m$ carrying current $I=4A$ as per figure given below is $\alpha \times {10}^{-7}T$. The value of $\alpha$ is _____. (Centre $O$ is common for all segments) 

Two charges of $5Q$ and $-2Q$ are situated at the points $(3a,0)$ and $(-5a,0)$ respectively. The electric flux through a sphere of radius $4a$ having centre at origin is:

The electrostatic potential due to an electric dipole at a distance $r$ varies as :

A capacitor is made of a flat plate of area A and a second plate having a stair-like structure as shown in figure. If the area of each stair is $\frac{A}{3}$ and the height is $d$, the capacitance of the arrangement is : 

Three capacitors of capacitances $25 \mu \mathrm{F}, 30 \mu \mathrm{F}$ and $45 \mu \mathrm{F}$ are connected in parallel to a supply of $100 \mathrm{~V}$. Energy stored in the above combination is E. When these capacitors are connected in series to the same supply, the stored energy is $\frac{9}{x} \mathrm{E}$. The value of $x$ is _____.

A capacitor of capacitance $100\mu F$ is charged to a potential of $12V$ and connected to a $6.4\mathrm{mH}$ inductor to produce oscillations. The maximum current in the circuit would be :

The ratio of heat dissipated per second through the resistance $5 \Omega$ and $10 \Omega$ in the circuit given below is : 

The effective resistance between $A$ and $B$, if resistance of each resistor is $R$, will be 

In the given circuit, the terminal potential difference of the cell is : 

Two wires $A$ and $B$ are made up of the same material and have the same mass. Wire $A$ has radius of $2.0 \mathrm{~mm}$ and wire $B$ has radius of $4.0 \mathrm{~mm}$. The resistance of wire $B$ is $2 \Omega$. The resistance of wire $A$ is _____$\Omega$.

In the following circuit, the battery has an emf of $2V$ and an internal resistance of $\frac{2}{3}\Omega$. The power consumption in the entire circuit is ______ $W$. 

The resistance per centimeter of a meter bridge wire is $r$, with $X\Omega$ resistance in left gap. Balancing length from left end is at $40\mathrm{cm}$ with $25\Omega$ resistance in right gap. Now the wire is replaced by another wire of $2r$ resistance per centimeter. The new balancing length for same settings will be at

Two resistance of $100\Omega$ and $200\Omega$ are connected in series with a battery of $4V$ and negligible internal resistance. A voltmeter is used to measure voltage across $100\Omega$ resistance, which gives reading as $1V$. The resistance of voltmeter must be _______ $\Omega$.

An electric toaster has resistance of $60\Omega$ at room temperature $(27^{\circ}C)$. The toaster is connected to a $220V$ supply. If the current flowing through it reaches $2.75A$, the temperature attained by toaster is around: (if $\alpha =2\times {10}^{-4}C-1\circ$ )

The electric current through a wire varies with time as $I={I}_{0}+\beta t$, where ${I}_{0}=20A$ and $\beta =3A{s}^{-1}$. The amount of electric charge crossed through a section of the wire in $20s$ is:

A capacitor of reactance $4 \sqrt{3} \Omega$ and a resistor of resistance $4 \Omega$ are connected in series with an ac source of peak value $8 \sqrt{2} \mathrm{~V}$. The power dissipation in the circuit is ________ W.

The coercivity of a magnet is $5 \times 10^3 \mathrm{~A} / \mathrm{m}$. The amount of current required to be passed in a solenoid of length $30 \mathrm{~cm}$ and the number of turns 150 , so that the magnet gets demagnetised when inside the solenoid is _____A.

The magnetic moment of a bar magnet is $0.5 \mathrm{Am}^2$. It is suspended in a uniform magnetic field of $8 \times 10^{-2} \mathrm{~T}$. The work done in rotating it from its most stable to most unstable position is:

Two identical charged spheres are suspended by strings of equal lengths. The string make an angle of $37^{\circ}$ with each other. When suspended in a liquid of density $0.7g{\mathrm{cm}}^{-3}$, the angle remains same. If density of material of the sphere is $1.4g{\mathrm{cm}}^{-3}$, the dielectric constant of the liquid is _____ $(\mathrm{tan}37^{\circ}=\frac{3}{4})$

An electric field, $\overrightarrow{\mathrm{E}}=\frac{2 \hat{i}+6 \hat{j}+8 \hat{k}}{\sqrt{6}}$ passes through the surface of $4 \mathrm{~m}^2$ area having unit vector $\hat{n}=\left(\frac{2 \hat{i}+\hat{j}+\hat{k}}{\sqrt{6}}\right)$. The electric flux for that surface is ______ $\mathrm{Vm}$.