Electromagnetic Induction Questions

A coil having $n$ turns and resistance $4R\Omega$ is connected in a circuit with a resistor $R\Omega$. This combination is moved in time $t$ seconds from a magnetic flux $W_1$ weber to $W_2$ weber. The induced current in the circuit is:

In a uniform magnetic field of induction $B$, a wire in the form of a semicircle of radius $r$ rotates about the diameter of the circle with angular frequency $\omega$. The axis of rotation is perpendicular to the field. If the total resistance of the circuit is $R$, the mean power generated per period of rotation is:

A metal conductor of length $1\text{m}$ rotates vertically about one of its ends at angular velocity $5\text{radians per second}$. If the horizontal component of earth’s magnetic field is $0.2\times 10^{-4}\text{T}$, then the e.m.f. developed between the two ends of the conductor is:

In an AC generator, a coil with $N$ turns, all of the same area $A$ and total resistance $R$, rotates with frequency $\omega$ in a magnetic field $B$. The maximum value of emf generated in the coil is:

The flux linked with a coil at any instant $t$ is given by $\varphi =10t^2-50t+250$. The induced emf at $t=3\text{s}$ is:

An ideal coil of $10\text{H}$ is connected in series with a resistance of $5\Omega$ and a battery of $5\text{V}$. $2\text{seconds}$ after the connection is made, the current flowing in amperes in the circuit is:

One conducting U-tube can slide inside another as shown in figure, maintaining electrical contacts between the tubes. The magnetic field $B$ is perpendicular to the plane of the figure. If each tube moves towards the other at a constant speed $V$, then the emf induced in the circuit in terms of $B,l$ and $V$ where $l$ is the width of each tube will be:

A coil of inductance $300\text{ mH}$ and resistance $2\Omega$ is connected to a source of voltage $2\text{V}$. The current reaches half of its steady state value in:

The self inductance of the motor of an electric fan is $10\text{ H}$. In order to impart maximum power at $50\text{ Hz}$, it should be connected to a capacitance of:

Two coils are placed close to each other. The mutual inductance of the pair of coils depends upon:

When the current changes from $+2\text{A}$ to $-2\text{A}$ in $0.05$ second, an e.m.f. of $8\text{V}$ is induced in a coil. The coefficient of self-induction of the coil is:

An inductor of inductance $L=400\text{mH}$ and resistors of resistances $R_1=2\Omega$ and $R_2=2\Omega$ are connected to a battery of emf $12\text{V}$. 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:

A rectangular loop has a sliding connector $\text{PQ}$ of length $l$ and resistance $R\Omega$ and it is moving with a speed $v$ as shown. The set-up is placed in a uniform magnetic field $B$ going into the plane of the paper. The three currents $I_1,I_2$ and $I$ (where $I$ is through the connector) are:

In a circuit containing a battery of emf $V$, a resistor $R_2$ in series with an inductor $L$ and resistor $R_1$ in parallel, the key $K$ is closed at $t=0$. The current through the battery is:

A coil is suspended in a uniform magnetic field, with the plane of the coil parallel to the magnetic lines of force. When a current is passed through the coil it starts oscillating; it is very difficult to stop. But if an aluminium plate is placed near to the coil, it stops. This is due to: