Which of the following statements is correct.

Briefly explain working of a.c. generator.

What is a dynamo? Describe an a.c. dynamo under the following headings:

$\left(\mathrm{ii}\right)$ Labelled diagram

A constant magnetic field of $1 \mathrm{T}$ is applied in the $\mathrm{x}>0$ region. A metallic circular ring of radius $1 \mathrm{m}$ is moving with a constant velocity of $1 \mathrm{m} {\mathrm{s}}^{-1}$ along the $x$-axis. At $t=0 \mathrm{s}$, the centre $\mathrm{O}$ of the ring is at $\mathrm{x}=-1 \mathrm{m}$. What will be the value of the induced emf in the ring at $\mathrm{t}=1 \mathrm{s}$ ? (Assume the velocity of the ring does not change.)

The phenomenon of electromagnetic induction has been technologically important application in the generation of alternating currents." Name the device which can generate alternating currents. Draw a neat diagram of it.

 A rectangular coil having an area vector $\overline{\mathrm{A}}$ and number of turns $\mathrm{N}$ is rotating in a magnetic field $\overline{\mathrm{B}}$ with angular speed $\omega$. If $\theta$be the angle made by the area vector $\overline{\mathrm{A}}$ with the field $\overline{\mathrm{B}}$ at time $t$. Derive an expression for alternating emf $\epsilon$ starting directly from Faraday's law. Draw a graph to show the generated e.m.f at the time   $0 ,\frac{\mathrm{T}}{4}.\frac{\mathrm{T}}{2},\frac{3\mathrm{T}}{4}\mathrm{and} \mathrm{T}$.

What is a dynamo? Describe an a.c. dynamo under the following headings:

$\left(\mathrm{iii}\right)$ Working.

With the help of a labelled diagram, derive the expression for instantaneous emf induced in an AC generator.

In a.c. generator induced emf at $\mathrm{t}=0$. the induced emf at the time $\frac{\pi }{\omega }$ is_____________.

A long straight wire carries a current, $I=2$ ampere. A semi-circular conducting rod is placed beside it on two conducting parallel rails of negligible resistance. Both the rails are parallel to the wire. The wire, the rod and the rails lie in the same horizontal plane, as shown in the figure. Two ends of the semi-circular rod are at distances $1 \mathrm{cm}$ and $4 \mathrm{cm}$ from the wire.  At time $t=0$, the rod starts moving on the rails with a speed $v=3.0 \mathrm{m} {\mathrm{s}}^{-1}$ (see the figure).

A resistor $R=1.4 \mathrm{\Omega }$ and a capacitor $C_0=5.0 \mathrm{\mu F}$ are connected in series between the rails. At time $t=0$, $C_0$ is uncharged. Which of the following statement(s) is (are) correct? [${\mu }_0=4\pi \times {10}^{-7}$ SI units. Take $\ln 2=0.7$]

Consider the situation given in figure. The wire $AB$ slides on the fixed rails with a constant velocity. If the wire $AB$ is replaced by a semicircular wire, the magnitude of the induced current will: