Electromagnetism PYQ — Page 66

In a series LCR circuit $R=200 \Omega$ and the voltage and the frequency of the main supply is $220 \mathrm{~V}$ and $50 \mathrm{~Hz}$ respectively. On taking out the capacitance from the circuit the current lags behind the voltage by $30^{\circ}$. On taking out the inductor from the circuit the current leads the voltage by $30^{\circ}$. The power dissipated in the LCR circuit is

In the circuit shown below, the key $\mathrm{K}$ is closed at $\mathrm{t}=0$. The current through the battery is 

A thin semi-circular ring of radius $r$ has a positive charge $q$ distributed uniformly over it. The net field $\vec{E}$ at the centre $O$ is 

If a source of power $4 \mathrm{~kW}$ produces $10^{20}$ photons/second, the radiation belong to a part of the spectrum called

The magnitude of the magnetic field $(B)$ due to loop $A B C D$ at the origin $(O)$ is

This question contains Statement-1 and Statement-2. Of the four choices given after the statements, choose the one that best describes the two statements. Statement-1: The temperature dependence of resistance is usually given as $R=R_0(1+\alpha \Delta t)$. The resistance of a wire changes from $100 \Omega$ to $150 \Omega$ when its temperature is increased from $27^{\circ} \mathrm{C}$ to $227^{\circ} \mathrm{C}$. This implies that $\alpha=2.5 \times 10^{-3} /{ }^{\circ} \mathrm{C}$. Statement 2: $R=R_i(1+\alpha \Delta T)$ is valid only when the change in the temperature $\Delta T$ is small and $\Delta R=$ $\left(R-R_0\right) \ll R_0$.

Two points $P$ and $Q$ are maintained at the potentials of $10 \mathrm{~V}$ and $-4 \mathrm{~V}$ respectively. The work done in moving 100 electrons from $P$ to $Q$ is

An inductor of inductance $\mathrm{L}=400 \mathrm{mH}$ and resistors of resistances $\mathrm{R}_1$ $=2 \Omega$ and $R_2=2 \Omega$ are connected to a battery of emf $12 \mathrm{~V}$ as shown in the figure. The internal resistance of the battery is negligible. The switch $S$ is closed at $t=0$. The potential drop across $L$ as a function of time is 

This question contains Statement-1 and Statement-2. Of the four choices given after the statements, choose the one that best describes the two statements. Statement - 1: For a charged particle moving from point $P$ to point $Q$, the net work done by an electrostatic field on the particle is independent of the path connecting point $P$ to point $Q$. Statement-2: The net work done by a conservative force on an object moving along a closed loop is zero

Due to the presence of the current $\mathrm{l}_1$ at the origin

A charge $Q$ is placed at each of the opposite corners of a square. A charge $q$ is placed at each of the other two corners. If the net electrical force on $Q$ is zero, then the $Q / q$ equals

Let $P(r)=\frac{Q}{\pi R^4} r$ be the charge density distribution for a solid sphere of radius $R$ and total charge $Q$. for a point ' $p$ ' inside the sphere at distance $r_1$ from the centre of the sphere, the magnitude of electric field is

A horizontal overhead power line is at a height of $4 \mathrm{~m}$ from the ground and carries a current of $100 \mathrm{~A}$ from east to west. The magnetic field directly below it on the ground is $\left(\mu_0=4 \pi \times 10^{-7} \mathrm{~T} \mathrm{~m} \mathrm{~A}^{-1}\right)$

A $5 \mathrm{~V}$ battery with internal resistance $2 \Omega$ and a $2 \mathrm{~V}$ battery with internal resistance $1 \Omega$ are connected to a $10 \Omega$ resistor as shown in the figure. The current in the $10 \Omega$ resistor is 

A parallel plate capacitor with air between the plates has a capacitance of $9 \mathrm{pF}$. The separation between its plates is ' $d$ '. The space between the plates is now filled with two dielectrics. One of the dielectrics has dielectric constant $k_1=3$ and thickness $\frac{d}{3}$ while the other one has dielectric constant $\mathrm{k}_2=6$ and thickness $\frac{2 \mathrm{~d}}{3}$. Capacitance of the capacitor is now

A thin spherical shell of radius $R$ has charge $Q$ spread uniformly over its surface. Which of the following graphs most closely represents the electric field $E(r)$ produced by the shell in the range $0 \leq$ $r < \infty$, where $r$ is the distance from the centre of the shell?

Relative permittivity and permeability of a material are $\varepsilon_{\mathrm{r}}$ and $\mu_{\mathrm{r}}$, respectively. Which of the following values of these quantities are allowed for a diamagnetic material?

Paragraph: Consider a block of conducting material of resistivity ' $\rho$ ' shown in the figure. Current 'l' enters at 'A' and leaves from ' $\mathrm{D}$ '. We apply superposition principle to find voltage ' $\Delta \mathrm{V}$ ' developed between ' $\mathrm{B}$ ' and ' $\mathrm{C}$ '. The calculation is done in the following steps: (i) Take current 'l' entering from 'A' and assume it to spread over a hemispherical surface in the block. (ii) Calculate field $E(r)$ at distance ' $r$ ' from $A$ by using Ohm's law $E=\rho j$, where $j$ is the current per unit area at ' $r$ '. (iii) From the ' $r$ ' dependence of $E(r)$, obtain the potential $V(r)$ at $r$. (iv) Repeat (i), (ii) and (iii) for current 'l' leaving ' $D$ ' and superpose results for ' $A$ ' and ' $D$ '. Question: $\Delta \mathrm{V}$ measured between $\mathrm{B}$ and $\mathrm{C}$ is

Paragraph: Consider a block of conducting material of resistivity ' $\rho$ ' shown in the figure. Current 'l' enters at 'A' and leaves from ' $\mathrm{D}$ '. We apply superposition principle to find voltage ' $\Delta \mathrm{V}$ ' developed between ' $\mathrm{B}$ ' and ' $\mathrm{C}$ '. The calculation is done in the following steps: (i) Take current 'l' entering from 'A' and assume it to spread over a hemispherical surface in the block. (ii) Calculate field $E(r)$ at distance ' $r$ ' from $A$ by using Ohm's law $E=\rho j$, where $j$ is the current per unit area at ' $r$ '. (iii) From the ' $r$ ' dependence of $E(r)$, obtain the potential $V(r)$ at $r$. (iv) Repeat (i), (ii) and (iii) for current 'l' leaving ' $D$ ' and superpose results for ' $A$ ' and ' $D$ '. Question: For current entering at $A$, the electric field at a distance ' $r$ ' from $A$ is

Two coaxial solenoids are made by winding thin insulated wire over a pipe of cross sectional area $A=$ $10 \mathrm{~cm}^2$ and length $=20 \mathrm{~cm}$. If one of the solenoids has 300 turns and the other 400 turns, their mutual inductance is $\left(\mu_0=4 \pi \times 10^{-7} \mathrm{Tm} \mathrm{A}^{-1}\right)$

A long straight wire of radius ' $a$ ' caries a steady current $\mathrm{i}$. The current is uniformly distributed across its cross section. The ratio of the magnetic field at $\frac{a}{2}$ and $2 a$ is

If $\mathrm{g}_{\mathrm{E}}$ and $\mathrm{g}_{\mathrm{m}}$ are the accelerations due to gravity on the surfaces of the earth and the moon respectively and if Millikan's oil drop experiment could be performed on the two surfaces, one will find the ratio $\frac{\text { electronic charge on the moon }}{\text { electronic charge on the earth }}$ to be

A charged particle with charge $\mathrm{q}$ enters a region of constant, uniform and mutually orthogonal fields $\mathrm{\vec{E}}$ and $\mathrm{\vec{B}}$ with a velocity $\mathrm{\vec{v}}$ perpendicular to both $\mathrm{\vec{E}}$ and $\mathrm{\vec{B}}$, and comes out without any change in magnitude or direction of $\mathrm{\vec{v}}$. Then

In an a.c. circuit the voltage applied is $\mathrm{E}=\mathrm{E}_0 \sin \omega \mathrm{t}$. The resulting current in the circuit is $\mathrm{I}=\mathrm{I}_0 \sin \left(\omega \mathrm{t}-\frac{\pi}{2}\right)$. The power consumption in the circuit is given by