NEET UG 2012 — Electromagnetism

In the circuit shown the cells $A$ and $B$ have negligible resistances. For $V_A=12 \mathrm{~V}$, $R_1=500 \Omega$ and $R=100 \Omega$ the galvanometer (G) shows no deflection. The value of $V_B$ is 

In an electrical circuit $R, L, C$ and an $\mathrm{AC}$ voltage source are all connected in series. When $L$ is removed from the circuit, the phase difference between the voltage and the current in the circuit is $\pi / 3$. If instead, $C$ is removed from the circuit, the phase difference is again $\pi / 3$. The power factor of the circuit is

If voltage across a bulb rated $220 \mathrm{~V}-100 \mathrm{~W}$ drops by $2.5 \%$ of its rated value, the percentage of the rated value by which the power would decrease is

A proton carrying $1 \mathrm{MeV}$ kinetic energy is moving in a circular path of radius $R$ in uniform magnetic field. What should be the energy of an $\alpha$-particle to describe a circle of same radius in the same field?

Two similar coils of radius $R$ are lying concentrically with their planes at right angles to each other. The currents flowing in them are $I$ and $2 I$, respectively. The resultant magnetic field induction at the centre will be

A cell having an $\operatorname{emf} \varepsilon$ and internal resistance $r$ is connected across a variable external resistance $R$. As the resistance $R$ is increased, the plot of potential difference $V$ across $R$ is given by

An alternating electric field of frequency $v$, is applied across the dees (radius $=R$) of a cyclotron that is being used to accelerate protons (mass $=m$ ). The operating magnetic field $(B)$ used in the cyclotron and the kinetic energy $(K)$ of the proton beam, produced by it, are given by

The current $(I)$ in the inductance is varying with time according to the plot shown in figure.  Which one of the following is the correct variation of voltage with time in the coil?

Two metallic spheres of radii $1 \mathrm{~cm}$ and $3 \mathrm{~cm}$ are given charges of $-1 \times 10^{-2} \mathrm{C}$ and $5 \times 10^{-2} \mathrm{C}$, respectively. If these are connected by a conducting wire, the final charge on the bigger sphere is

A coil of resistance $400 \Omega$ is placed in a magnetic field. If the magnetic flux $\phi(\mathrm{Wb})$ linked with the coil varies with time $t$ (sec) as $\phi=50 t^2+4$ The current in the coil at $t=2 \mathrm{~s}$ is

The ratio of amplitude of magnetic field to the amplitude of electric field for an electromagnetic wave propagating in vacuum is equal to

The instantaneous values of alternating current and voltages in a circuit are given as $$ \begin{aligned} & i=\frac{1}{\sqrt{2}} \sin (100 \pi t) \text { ampere } \\ & e=\frac{1}{\sqrt{2}} \sin (100 \pi t+\pi / 3) \text { volt } \end{aligned} $$ The average power in Watts consumed in the circuit is

A parallel plate capacitor has a uniform electric field $E$ in the space between the plates. If the distance between the plates is $d$ and area of each plate is $A$, the energy stored in the capacitor is

A ring is made of a wire having a resistance $R_0=12 \Omega$. Find the points $A$ and $B$, as shown in the figure, at which a current carrying conductor should be connected so that the resistance $R$ of the sub circuit between these points is equal to $8 / 3 \Omega$ 

A magnetic needle suspended parallel to a magnetic field requires $\sqrt{3} \mathrm{~J}$ of work to turn it through $60^{\circ}$. The torque needed to maintain the needle in this position will be

In a coil of resistance $10 \Omega$, the induced current developed by changing magnetic flux through it, is shown in figure as a function of time. The magnitude of change in flux through the coil in weber is 

The power dissipated in the circuit shown in the figure is 30 Watt. The value of $R$ is 

What is the flux through a cube of side $a$ if a point charge of $q$ is a one of its corner?

The electric field associated with an electro magnetic wave in vacuum is given by $\mathbf{E}=\mathbf{i}$ $40 \cos \left(k z-6 \times 10^8 t\right)$, where $E$, $z$ and $t$ are in volt/m, metre and second respectively. The value of wave vector $k$ is

A millivoltmeter of $25 \mathrm{mV}$ range is to be converted into an ammeter of 25 A range. The value (in ohm) of necessary shunt will be

Four point charges $-Q,-q, 2 q$ and $2 Q$ are placed, one at each corner of the square. The relation between $Q$ and $q$ for which the potential at the centre of the square is zero, is

An electric dipole of moment $p$ is placed in an electric field of intensity $E$. The dipole acquires a position such that the axis of the dipole makes an angle $\theta$ with the direction of the field. Assuming that the potential energy of the dipole to be zero when $\theta=90^{\circ}$, the torque and the potential energy of the dipole will respectively be